Here are a few more tweaks to the strategy.
Of your first three cities (two settled, one captured) it is ideal if you can task two for immortal pumping (this is more about chopping forests than hammers initially, although hills will be beneficial later on) and one to be a science/commerce/wonder city. The science city should have plenty of river squares, and gold is a good thing. Whenever its convenient move your palace to the science city. Skip the barracks and the court house here and go for library, monastary, etc. Probably build the oracle here so you don't disrupt the war effort. The science city is important, so I wouldn't hesitate to chop out a settler if I couldn't find a suitable city for the taking. But I haven't had this problem. Usually my starting city or some other nearby civ's starting city is a good fit.
After bronze, research writing. All the civilizations will sign open borders with you so you can more easily steal their workers and case them for future conquest. Find all the bronze - you must control it or wait until you get catapults for that civ. I found it helpful to leave the civilization in the middle for last, because it was so convenient to slide over their nicely built road network. It's also nice to converge on it from all sides in the end-game (catapults/axemen are _slow_) Of course if you attack their friends they are likely to pull their open borders agreement, so a little diplomacy is helpful here.
Then research (masonry if you have marble), mysticism, meditation, priesthood. Chop rush the oracle and get code of laws and probably Confucianism. Spread confucianism to your science city if it doesn't already have a religion. Adopt whatever religion your science city has; build a monastary there. Chop rush courthouses in all your conquered cities. You can chop rush a court house while the city is still in rebellion and not building anything itself. You might want to adopt the caste system so you can force scientists or merchants to work in your captured cities. This can be a good way to keep your science/gold going, prevent the city from growing beyond its happiness limit, and pump great scientists/merchants for your science city at the same time.
Then it's pottery (start building cottages all over your science city), masonry, mathematics, construction. Those catapults are going to come in handy by now.
After this in no particular order I suggest:
Civil Service - Bureaucracy will jump start your science city (move your palace there!)
Monarchy - bigger cities through happiness induced by armies.
Iron Working - you don't _need_ swordsman, but you want to keep the AI from getting them; prior to this you might want to pillage all mines just in case.
Random points:
If you have the choice of more than one horse resource, remember that you can trade along rivers - it's less work and rivers can't be pillaged by barbarians. Pick the horse that can be quickly networked to your capital. Take full of advantage of rivers when networking newly conquered cities.
You can bypass one city hill civilizations by dedicating an immortal to pillage and harrass them. You can fortify on the square next to the city (preferablly a hill) with impunity as their archers can't hurt you. This can be better than burning a bunch of immortals on a charge up a hill just to get a sorry city you would burn anyway. Watch their build up by hovering your mouse over their city. Eventually they will build a two archer + 1 settler group and send it out. Take it out to capture another worker and prevent their growth. The AI will prefer hill locations for their defensive value, so expect them to head to a hill not far away from their besieged city.
Be picky about the cities you keep. I will keep most capitals and burn the less developed cities unless it is a particularly good location or a holy city. Remember unlike the Roman you will pay full price for courthouses so you need a wide area of trees to chop for them. Also you don't want to be prepping more than one or two conquered cities at the same time; the pressure on your gold will be too much. Keep the best and burn the rest.
Don't let your gold go all the way down. Sometimes you will have deficit economies that you can't overcome except by having a warchest. You will have to micromanage your science bar to keep the war effort going. Judge how many turns you are from conquering another city and set your science accordingly. If you mess up anarchy can be a way to stave off an impending gold crisis/strike. Just pick some available civic and revolt - then keep chopping out those courthouses.
