I will try to address all your responses below, but would first like to make a couple of general points. Although I've mentioned various concepts/strategies they are not meant to be cookie-cutter. CIV, as I'm sure you've ascertained, is a complex game that has many approaches. There are, I believe, some golden rules in the game, like the importance of workers and granaries - and food, but a lot of other strategies can be situational depending on a variety of factors like the map(land), difficulty, leader, opponents, and even game speed, among other things. Also, Vanilla is not well played anymore. BTS is a much more evolved version of the game, so some of things I mention may not work quite the same on Vanilla. Conversely, some of the strat articles you may have read were based on the vanilla game or Warlords, so some of that advice may be outdated like the infamous 60% slider rule.
I couldn't find a better city than Olla for HE, since there aren't any cities with hills that have enough grass or FP. What I did do, though, bc I didn't want to wait to take advantage of Financial, was to cottage the jungle tiles south of that city as soon as the borders popped so I could gain commerce while waiting for production. My first war didn't net me a 10xp unit anyway (I had 2 at 9 that died on their next attack lol).
I've been too lazy to pull out the ole Vanilla cd to check the land in your game. If Olla is truly your best production city then it might be best to groom it as such. In that case, farms might be of better use early so that you can work the mines you can build and also use whipping as production. Farms will allow the city to still grow nicely so that it is fairly large by the time the hammer improvements kick in. When you have extra worker turns available at some point you can start putting up workshops on certain tiles with the expectation that the city will grow on them later. You can also run specialists in the city to counter-act growth when you hit the happy cap and are not whipping.
Alright. Am I hearing that there is some value to smaller cities that have, say, just one resource (a gold tile, or a fur tile, for example), since they will produce at least a few beakers? I tend to stop adding cities even if I could squeeze them in thinking they might be too expensive. I'm talking about ones that don't have enough food to use enough hammers to produce a Courthouse in under 20 turns, let alone Market/Grocer/Bank.
I'm a little confused on this particular response in terms of the context of the original discussion. It does lead me to two possible points of discussion:
1) Don't settle a city just to settle a city. Early game settling a city with Gold is a good idea for early commerce even if the city is not that great. Hopefully it will have some food or something to make it decent, but just working the gold for a while is good. More important settle for resources and land. Ideally you want to block of land in such a way that you serve both purposes, but you don't always have that luxury. Regardless, you want your first cities to be productive in some way, either via food, production, strat resources and commerce. I focus on commerce last usually, but a gold or silver tile to work early on higher levels can be nice. Food and production though allow you to fuel expansion either by peace or war. And again, food is production.
There is nothing wrong with a nice tight empire of 6 cities by 1AD.
2) CHs are not needed everywhere, especially cities close to the cap - so that would not be my concern. Markets/Banks/Grocers are "specialized" buildings that you don't build everywhere - usually only high commerce cities. Markets/Grocers do provide happy/health bonuses but you really don't need that early to mid-game and certainly check to make sure you have the bonus resources. Just having 1 or even 2 of them may not make those buildings worth it outside high commerce cities. Building these buildings in such a way is called "over-building". Put those hammers to other uses.
Oh...and whipping can usually get in the stuff you need quickly.
I have been taking some advantage of trading extra resources (3rd gold, 3rd spices, 2nd cow, etc) for gpt. I sometimes beg for old techs (for example, when I don't have a religion, I tend to completely ignore Myst/Mono/Priest, and those are often given to me when I get closer to running to Lib), but rarely for wealth. I'll start trying that more often.
Not sure what you mean by "3rd Gold, 3rd Spice". If I have any extra resources, I'm either trading them for gold or other resources. You should not have ANY extra resources if you can trade them. Resource benefits do not stack - you only need 1. Trade your only copper if you have iron and the AI has iron. I've even traded horses if I don't plan to use them. Heck...I'll even trade an only health resource for gold if I'm EXP or health is not really a concern - same with a happy if I"m Char or otherwise doing fine with happy (Hereditary Rule), although I usually want to keep an only happy resource since I whip A LOT.
I would avoid begging for Techs. This increases your "We Fear You are Becoming Too Advanced" threshold, which makes trading for techs harder later. Begging for gold does not . Trade techs for techs and balance trades with gold. You can often trade 1 monopoly tech for many backfill techs from the AI. Try to spread tech trading around and, of course, beware of what you trade to your rivals. Not that you should not trade with them, but don't give them something that will give them an advantage as you are going to attack. Ha....I do trade techs with AIs I'm just about to attack though. Might as well get something from them before destroying them. Also, you can get techs in peace deals.
Not sure how you can ignore Myst for so long unless you are creative. Early border pops are often very important. Mono is a good early tech to backfill to get the powerful Organized Religion civic if you are running a religion. OR is one of the best early civics in the game. (Not saying you need to tech Mono, but it should be pretty easy to pick up in a trade not long after Alpha kicks in). Priesthood? Don't you ever build Oracle?
Binary research. I've definitely heard this phrase several times, but it's always been a little frightening to me. Remember I'm already running 0-20% during Mach/CivSvc too often, so decreasing my slider seems counterintuitive. I do drop it down to 10% purposely when warring, but I always considered war just a phase of the game where different priorities take over, not as something I could consider duplicating parts of (eg, lowering the slider) during other phases.
Binary is a more advance concept as are some other things I've mentioned. It does take time to get more comfortable with these things. However, you do seem to have a lot of economic issues that I think you need to practice/work on. I usually don't sit and "view" my game at a certain point as "0 to 20%" slider. It just does not work that way for me. There are so many ways to fund deficit research. I rarely run my slider in between 0 and 100% except very early game when you start settling a couple of cities and the maintenance start kicking in. Later, I might adjust it around a bit for balance to get a tech in, sure, but I don't think in terms of..."heck, I can only run at 20%". Once you get past this blocking point, it will totally change how you play the game.
I already have Oxford in this game (the Huayna Capac one; I even got the Great Library, very rare for me!), so next game I'll specifically run 0% research while I'm building libraries, with Alpha as the tech in the window. I presume you normally research Writ before IW unless there's no available bronze, right? Same argument as (part of) Curr: trade routes.
I going to offer a bit of advice at the end to address the slider issue among other things. As for IW, I RARELY tech it myself except if the map absolutely calls for, i.e, tremendous amount of jungle and jungle resources (think gems,bananas) that I must expand into. Otherwise IW is VERY easy to trade for after you get alpha. It's a waste of beakers to tech outright unless you have to have it.
Not totally clear on your comment about Currency. It is something I try to get as soon as I can by either teching outright or trade for it. Don't forget that Math gives a bonus on Currency (not sure if you are aware of the tech predecessor bonus), so you want to trade for or tech Math on the way. The exception to this is simply other strategies in the game, like going straight for the Great Library or something else. Still you can always trade for these things. The key is not teching what the AIs tech to set up trades.
AIs tend to always prioritize certain techs in the game like Maths, IW, Machinery, Feudalism, Engineering. Only tech these straight up unless you have a specific reason/strategy for doing so. Machinery can be bulbed by a GE or GS if you are looking for early Xbows like for a UU.
Over time you will learn to balance your tech path with tech trading.
Edit: Oh...another point on Writing. Taking out the whole "wrong" IW/Writing comparison that I already mentioned, that is, I rarely tech IW, Writing should anyway be one of your earliest techs - probably first 4th to 6th tech depending on land or if you go Oracle. Prioritize Worker Tech>Strat Tech>The Wheel>Writing (which means POT or AH before). There's variants based on several strategies to this but Writing is still always in the mix among your first few techs - it is SO important to get at least that first library up and 2 scientist running, not to mention Open Borders, diplo, and trade routes. If you don't reveal Bronze or Horse, deal with warriors until you can trade for IW later or bite the bullet and pick up Archery, but get Writing asap.
I'm a little more hesitant to run 0% right after Edu, since I'm usually racing to Lib. By this point I usually have 2 scientists in whatever city I'm planning to place Oxford, and usually 1 in 3 or 4 other cities. (I'm also often running Respresentation, bc I often get the Pyramids.) Is that enough or should I still fear losing the Lib race, and switch to 0% after I get Lib? I think it sounds like the latter, since Univs are never around before I get Lib anyway.
Do what you feel is best for the game. However, note that I usually either part or full bulb Education, so I get it fairly early. I also mass whip my 6 Unis - we are talking around a 4 or 5 pop whip here to get them in asap. Not all cities may need a 4/5 pop whip, like the cap. I will also do whatever I can to get Ox up in the Bureau cap or whatever city has been set up best for it. Hopefully you have stone or trade for it, but I will even whip it in as well, though you generally don't whip wonders. So you might have the luxury of running some binary here, while using Lib as a placeholder. Ha...my "luxury" to do this can vary quite a bit on IMM and Deity, but then my economy is usually in better shape than yours as well - that will change though

.
Another thing I do is often tech Lib to 1turn of completion and try to go for a more advance tech. You just have to note where the AIs are in terms of the Lib race. Instead of Libbing say Nationalism, I might tech Nat and Lib Military Tradition to get Curs up and running asap. Or tech Chem and Lib Steel. Cannons absolutely rule Vanilla and Warlords.
With a few adjustments to your game you should starting raping the AIs in tech.
Oh...and Mids. Unless you are IND or have stone, you really have to ask yourself if it is worth the rather large hammer investment. Early Rep is nice but I found often that less experienced players aren't even using it correctly. Running 3 or 4 specialists is not making Mids worth the investment.
GMs are valuable! I only ever get them if I get both the Great Lighthouse and Colossus, otherwise I always produce GEs and GSs. When I get one, I always look up whichever city is closest to the top in the Top 5 Cities screen, but furthest away, and send him there. I've taken advantage of the wealth boost he gives, but not purposely. That's just a blind spot in my technique. This also explains why everyone loves Caste System but I rarely use it: I've got libraries for scientists, sometimes Observatories, and don't want merchants/artists (til now).
Caste System is very powerful. The hard thing on Vanilla/Warlords is anarchy if you are not Spiritual. Spiritual is still a good trait in BTS but was very good on the older versions because of this, since you can easily temp switch to Caste for several turns to pump out Great People - even starving cities to do so. In BTS, you now get "no anarch" from Golden Ages. Even better, you get a bonus to GPP (Great People Points) during a Golden Age. So often I will run a Golden Age, switch to Caste, starve my NE city and maybe other cities that can get out GPs fast and pump out 2, 3 or 4 GPs in 8 to 10 turns. Great way to bulb Edu or get GMs to fund something like a mass Cur upgrade. Still, it may be worth the anarchy in Vanilla to get out a few great people early, but often you want to get back to slavery as soon as you can.
My 1st several GSs go into Academies, 1st couple GEs go into wonders if possible (I like the Hanging Gardens and Statue of Liberty especially, beyond the Pyramids), and I rarely generate other types. GAs are saved for war expansion if they ever come up. I'll purposely focus on GPs, of course, if I have a religious city. I rarely use them to learn techs; Phil if no Taoism, Edu semi-regularly, Steel (I think GEs do steel) if a war is coming against a superior foe, not much else.
Unless going for Culture, GAs hold little value other than using them to kick-off Golden Ages, which are nerfed a bit below BTS, but still valuable. I would not go out of my way to get GAs, but realize that certain wonders do have GA points so you are going to get one now and them. More often than not, if you are founding a later religion like Conf or Tao, the shrine is not worth going out of the way to get a GP. If a GP does happen to pop, I may consider creating a shrine, but I'm not going out of my way to get him. Better to conquer an established Hindu or Buddhist Shrine city - cha-ching! GPs do have very good "settle" value, especially if you are running an SE economy. One of the better "settle" outputs for a great person. Still there generally pretty worthless for bulbing unless playing a strict religious type game.
In certain strategies, GEs have some decent bulb opportunities mid-game but yeah, their main worth is for rushing wonders. However, later game you usually have pretty good production cities to get out wonders. I would generally not rush wonders if I have the bonus resource or I'm IND as it is actually a waste of hammers. Still it may be worth to rush a specific wonder based on strategy or necessity like The Taj or even Ox itself. GEs can be good to settle if running and SE or WWE economy. (you usually settle most great people anyway in those economies)
Otherwise, GSs (early) and GMs (late) are the most valuable great people. Learn to use them. Bulbing GSs early/mid-game(pre-Lib or Astro) can be huge. After than, not so much - like a GE on Steel is not generally a good idea. Lib Steel if you want it fast. Late game, settle great people, run Golden Ages or focus on GMs for trade missions.
Also, note that BTS as Corporations (think a late game religion system with Corps) that are founded by Great People.
Academies - Generally you need only 1 in your capitol usually. Depends on the timing of the GS and bulb potential. I don't always create an Academy with the first GS but I usually do and you probably should do so for now. However, "several" academies is concerning. I question if you are putting these in cities that even warrant an academy. Instead, look for bulb opportunities like Philo and Educations or maybe even settling the GS in the 1st academy city. Definitely valuable under Rep.
To sum up, then, the slider just isn't that important. Scientists can provide beakers even at 0%, trade routes and resource trades can produce wealth elsewhere, and it can be a valuable thing to build up a money base, even during non-wartime. Should I ever worry about too much money, when the AIs come begging?
Sorry, not meant to say the slider is not important. What is important is how you use it. Balance gold generation to what you need to get a tech in. No you should not just hoard 100s and 1000s of gold. You want to use the gold as soon as you can for research, trading or whatever. It is all about balance and it takes a bit of time and practice to get a handle on it. The most important thing is having a strategy and sticking to it or at least being flexible enough to adjust when needed.
One last question. If I have more wealth bc of a strategic 0% slider, do you ever use that extra money to upgrade units, or is it too expensive for the gain? I like to upgrade Swords and Mace to Grenadiers for the city-attack promotions, and sometimes cats to cannons, but rarely upgrade otherwise.
Good question. Upgrade judiciously. It's all situational. I definitely want to upgrade those CRII or III swords/axes to Rifleman or whatever, as it's a promo that does not exist for those units but actually works nicely for them if they have it. Heck, I've even been at a point of finishing Rifling, but pumping a few mace out of my HE city with a settled Great General (ha...not in Vanilla) for a 2 promo Mace out that gate that I give CR II and then upgrade to a Rifle. However, I'm certainly not going to waste money on upgrading a bunch of warriors or archers that have been sitting around for 1000s of years doing nothing. (oh...note on Archery...another waste/dead end tech...try not to tech it directly if you can...usually easy to get away without archers below Deity...you can always trade for it later)
Another thing is to strategically setup mass upgrades at a point of military tech advantage, such as getting Military Tradition or Science. (I don't use Grens much in BTS). I like mounted units or Rifles/Cannons. Anywho....as you are about to get your strong military tech lead, also look to build up a huge wad of cash via a combo of some turns of 0% slider, Great Merchant mission, begging and trading techs for gold. Meanwhile, pump out lesser and cheaper units like horse archers>Curs/Cavalry or mace for Rifles/Grens or even cats>Cannons. By the way, siege units are uber over-powered on Vanilla/Warlords - make sure you are using them unless going straight mounted warfare. Cannons can wipe the map. Siege is still hugely important in BTS, but siege does not kill. Then upgrade all these units and go stomp someone.
In closing, and as referenced, I wanted to make another general comment or piece of advice. There are a lot of concepts discussed here and it is a lot to take in. You are certainly not a newb, but you have played the game for some time without really improving (I was the same way at one point). Try not focusing on all these concepts at once, but rather roll a game with a decent start/leader, make sure you save the start, and play the first 100 turns over several times to practice a particular concept. Then when you feel comfortable, add in a bit more. The first 100 turns are always the most important anyway, so it is good to get comfortable with it. Then try another series of 100turns on another map/leader. of course, you can finish one of these games whenever you see fit, but I would focus on replaying the first 100 turns several times first. Once you get comfortable there, things will steamroll later.
Also, check out the Strategy and Tips forum. Get BTS (and BUG/BULL or BAT mod) and playing along with some forum games like Nobles Club and just generally peruse the forum or ask questions. Once you get BTS, you can even post your own "shadow" game.
Another great thing is to watch Let's Plays on You Tube. I have one completed for Mehmed which you can find in my sig. However, guys like Absolute Zero and TMIT have a ton of good ones that you can find in their sigs as well. You can learn a lot of tips and tricks from them.