Holy Crap! I started typing and just couldn't stop ... talk about information overload!
I thought about deleting it, but didn't want to make all that time a wasted effort ... I'm sorry.
And look what I found in my BFC! I decided to hook those babies up right away.
I

Chariots!
A side note about difficulty: At Prince and below, AI civs start without Archery, so at least for the first ~3000 years, the chances are very high of finding a Capital city protected by only one or two hapless Warriors.
This is especially important against Protective civs and those with early UU Archers (like the Bowman), since catching them without Archery means their UU and defensive traits are worthless against you.
Regardless of difficulty, when AI Civs learn Archery, the Chariot's reign can quickly go the way of the dinosaur.
The #2 reason I like Chariots are for their promotion lines. My Chariots almost always end up with Flanking -> Sentry for super fog-busting and scouting or Combat I -> Medic I,II,III -> March for M*A*S*H duty.
What do you think of this stack? Is it enough to take on Hammy? Or should I hold off for a bit and build more units? Or should I go after someone else entirely? I like the idea of Hammy, because he has a couple of nice cities and he has a holy city.
I think you should target your stack directly at Babylon. You'll likely sustain very heavy casualties, so the reinforcements you're constructing now will become the bulk of your force against the remaining Babylonian cities.
If you're lucky and don't lose too much of the initial stack, the reinforcements can raze the city west of Babylon (Akkad?) while the remainder of your initial stack can raze Nippur. Then, the remainder of the force can converge on the city south of Babylon and finish off Hammurabi.
Here are my cities. I hadn't planned on building any wonders this early, but for my sanity, I need the Great Wall to keep those nasty barbarians out. I just hope I haven't started it too late.
I think building the Great Wall is the smartest thing you can do in an all-out Conquest/Domination game, because it essentially eliminates one of your opponents (The Barbarians). Units which would have been committed to fog-busting and defending the homeland can be focused at the front.
I'm a little lost about a tech path to take.
IMO:
- Iron Working is key to knowing where and what to pillage first and for Swordsman (and your UU).
- Code of Laws is key for keeping captured cities.
- Currency is key for the extra trade routes, the ability to sell your extra resources to neighbors and for Markets in your Commerce cities.
- Mathematics is key for more lucrative chopping and to open Construction.
- Alphabet is key for Spies (specifically for improvement sabotage & city revolt).
- Construction is key for Catapults and Jumbos.
- Horseback Riding is key for Jumbos and Horse Archers.
- Metal Casting is key for Forges.
I think you're doing very well without outside influence, so beelining Construction seems like the best approach to me.
And since I'm not doing the builder route, I wondering what basics I need in my cities. Barracks? Graineries?
Treat every city just like you normally would (as far as specialization is concerned):
Bibracte is the production powerhouse (20 hammers @ pop 7), so it gets Barracks & Granary.
Vienne and Madrid have good production and good riverside grasslands, so they seem best suited as production-commerce hybrids with Barracks, Granary, Market & Library (with priority on the Market).
During rebuilding periods or during the war if money gets tight, you can switch Vienne and/or Madrid to Riverside Cottages to prop up your economy.
Babylon has decent food and production and plenty of Grassland, so I'd probably turn that into a pure Commerce city with Granary, Market & Library.
With so few cities and a high

slider, I think Babylon is the only city you should prioritize a Courthouse in for now. Around the time you acquire 6 cities and your peacetime science drops below 60-70%, you'll want to start putting Courthouses everywhere.
Dont' promote units before you need it.
QFT. Most of the time, you don't want to promote your unit until the turn before combat to ensure you use the best, most applicable promotions.
Delaying promotions [until after combat] can also be of great tactical advantage since every promotion heals the promoted unit by +50% of the remaining damage:
For example, let's say you can promote your Axeman (3/2 XP) to CR1 before attacking a city. His unpromoted odds are 90% to win, so you attack without promoting. He wins but takes heavy damages and is now at 1/5

& 5/2 XP. In this same turn, you can now promote the Axeman to CR1 to bring him to 3/5

& 5/4 XP and then again to CR2 to bring him to 4/5

.
Though it's a gamble against lower odds, this can protect the unit from counterattack, ensure shorter downtime from healing and give the unit a chance to re-enter the battle on the next turn if necessary!
Before you attack your next target, make sure to scout out his strategic resources (horses, bronze, whatever else you can see at that point) and plan on a resource-denial squad to raze them.
QFT. Knowing your enemies' resources also clues you in on what kind of units you're likely to come up against.
It's hard to build the "perfect" resource-denial squad, but Combat/Shock-promoted mounted units tend to do the trick for me. Most of the time, I lose at least one of the units, but denial of that resource is well worth it, imo.
Once you have Alphabet, you can build spies to knock the resources out.
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Gilgamesh and Cyrus are the only Civs without a holy city, so every capital but theirs has at least +60% defense from culture alone -- meaning they are largely untouchable until after Construction.
However, Gilgamesh is Protective, and so is also an untouchable pre-construction.
That leaves only Cyrus as a viable candidate after Hammurabi. If you throw everything you have and will have at Cyrus (especially if he's defending with Immortals against your Spearmen), you might have a chance to take him down now.
Whether you go for it now or not, it looks like you might be on hold until you can get Construction.
EDIT: I originally recommended side-tracking towards Priesthood for a shot at The Oracle, but I'm not sure if it's worth gambling away precious research and hammers simply for
a chance. I think it's more prudent to put it towards a sure thing, so hopefully you didn't take this original piece of advice.
During the time you're "on hold" waiting for Construction, prepare for the beginning of the end:
- Scout your enemies.
- Build up the bulk of your attack force accordingly.
- Build roads to your enemies' doorstep.
- Pre-chop forests around Bibracte and Madrid.
As soon as you discover Construction, begin finishing a Forest per turn in Madrid and Bibracte until you have a massive force of Catapults ready to bang the drums of war.
Once you get started, it's very likely you won't have to stop at all!
-- a whole lot more of my 2
