Yes, you make warriors in those first 50 turns. Indeed 5 turns for a warrior and 5 for a worker as said. But those are the warriors you have to build because you won't have the food to start with a worker anyway.
Those warriors that you HAVE TO build are all that you need really.
And yes, i also start with barracks before i have all cities i want, but if there is no AI in my way, it won't be before turn 50.
Either this means i have a settler factory that builds most of my settlers and i just build 1 - 2 extra settlers in the first towns i make, followed by workers in every town and then barracks in those first towns and more workers in the border towns. It gets to turn 50 then before i'm building those barracks.
Without settler factory, i simply build settlers wherever possible and around turn 50-60 would be a normal time to reserve the first cities for barracks.
Doing so any earlier while it is not needed just hurts your growth rate too much. I know how i learned to do it this way. When i started playing civ, i didn't feel safe without an army, I dreamed about pretty pyramids and I figured I should get libraries fast. That was all wrong, but i remember how you feel
I'm sorry obormot, i know you're a decent player and poster, but really, i feel 100% sure about what i say about early growth. Anything one sais about the importance of early growth in civ3 can only be an understatement. And early libraries is an awefull choise.
Your new city placement looks better, although i would have certainly placed 3 cities on that river at your capital.
You still need more workers, but you're getting in the right direction. It's just that i see Atlanta without improved tiles.
I also don't know what you are doing wrong exactly on growth, but it can be quite a bit better. you have 21 citizens now at 1000BC, no problems with Jungles and even a food bonus. I Think around 1000BC it is normal to have citizen counts around 30 in a starting area like this. (around 50 for the optimal situation of an agricultural civ with food bonus at capital).
I now count 7 workers, and they are almost enough to keep all your used tiles worked. Note, if you manage to improve your growth rate, you will have more citizens and need still more workers. If you had those 30 citizens, you would need 12 or so workers. And yes, that is possible.
Now about technollogy:
There are some technologies the AI very much likes to research, these are the following:
-Map Making
-Feudalism
-Invention
-Gunpowder
-Nationalism
-Replacable parts
-Flight
Map making is about 4 or 5 times as likely to be researched as the other techs after writing, Feudalism is an ever stronger favorite, 6-7 times as favorite as the other 2 MA starting techs. Invention and Gunpowder are strong enough favorites to be sure that at least some of the AI will research them imeadiately, so you never have to research these yourself. The last 3 are a virtually sure choise for the AI.
Those they do NOT like:
-Literature
-Currency
Literature is really low priority for them, Certainly at higher difficulties. On Sid, it is not strange to have all 7 AI's enter Industrial age while still not having Literature. This is the best research if you want a monopoly on one. Philosophy isn't high priority either, so your chances for a free tech there are also pretty decent.
Currency is not a huge underdog in the AI's choises, but i simply mention it because it is usually the best choise of research in AA and is significantly less chosen by the AI than construction.
So i would suggest to research Literature and trade for Map Making. Map Making is a more expensive tech and you can't trade them 1 on 1, but if you wait until they spread it amongst eachother while you are still the only one with Literature, they will give it for Lit.
Now a few small notes:
-Why not place SF one tile South-East? It is still on river and coast, it takes more water there, and you will still have acces to all the same land tiles you have now.(Don't look at how many land tiles are in the cities own radius, if that is 6 or more, it is ok. Rather look at your empire wide tiles available. You can shift tiles between cities anyway)
-Same for NY, 1 SW.
-Chicago is building a granary, but it has barely any food. A granary is not a solution for a food poor city. It sucks at that. Instead, build granaries in your rich cities.
-You seem to be building granaries everywhere now. I am usually much more selective about those. Build them in cities with food bonus or cities that have a huge production and simply make many more shields than 30 in the time needed to grow 2 citizens. This usually makes me build 3 granaries during my expansion phase. This is the easiest way to translate the "whatever makes most FPT" principle into simple actions: Build granaries in cities with food bonus and build granaries in cities with production that significantly exceeds their growth rate (if just 10 shields too much, you could build a warrior between settlers)
For more granaries, i prefer to conquer the pyramids if they are on my continent, else i build them usually after my warmachine is running or not at all (if i plan to win early).
In my games, i would now usually be building barracks in all my cities, (while having 2 or 3 completed earlier, those, as i said i start building around turn 50-60) However, in my games, i have neighbours to fight
I see no AI's in your games or they are very remote. First of all, that strenghens my statements about growth early on. If noone bothers you, more reason to keep building those settlers. Normally i can't state turn numbers for when to start building millitaire so easilly because one might be faced with an agressive neighbour very closeby, but your games all have plenty of space, therefore, i now do state those numbers. If you run into a game with a closeby AI, you might need to start your first barracks earlier than turn 50-60. It will take a little practice to estimate how late you can build them without getting yourself in danger, but you should realise that your goal is to start them as late as possible and keep growing as long as possible without endangering yourself too much.
I guess you make games with fewer than the default number of AI's. While this gives you plenty of space, it also provides a kind of vacuum in your games, wich is right now. You have plenty of space to continue growing, but your cities will all be corrupt so it will have to become ICS area. You could now be ready to go for war, but there is noone in the neighbourhood to fight with. It is nicer if your opponents are just 2 steps away and have roads trough their empire that you can use.
I am currently playing a PBEM game where i have the save files of every single turn from the early game. Those could be good an example for you. About city placement, about what to build in those cities, and when you have to start building military against deity closeby neighbours. (Meaning it will be less urgent in your games). While in a PBEM game there are of course other influences (a human opponent) that are missing in the single player games, this particular game started out very similar to single player games because of the large distance between us and the presence of 6 unusualy strong Deity AI's.
If you send me an email or PM with your email adress, i will put them in a zip file and send them to you. I only ask you not to say 1 word about the actual game in the forums because it is a game still in progress and my opponent reads these boards

You can email or PM specific questions instead.
And lastly, i see you added a picture of your demographics. I figure i'll give you the link to an explanation about them. So you know what they actually mean.
http://www.civfanatics.com/civ3/strategy/demographics.php
Family size is the one you should be #1 on
