In the early game, the first Three cities should be thus:
Capital, either production based (Early Unit Pump+building Research) Food based (Build Library, run scientists, whip) or Coin Based (Money, and almost just money, it woun't grow way past the happy cap probably)
Production City+Military Resource: A Military Resource often gives high Hammers by itself, and a few surrounding hills, at least one food resource, and you can build constant MILITARY except for gaps for Granary, Barracks, Forge and the ociational Happy/healthy building
Worker Pump: If you get 2 Food resources and 1 Plains hills you are good to go. Even with 2 Plains Cows, that is 8 food, 7 hammers with 3 pop, and that gose into 9 production of Settlers and Workers by itself! With 2 more grassland hills and 1 Farm, at 6 pop you will have 13 food and 13 hammers, a total of 14 production of settler/worker! At the earlier pump it is Worker (7 turns, 3 overflow) Settler (12 turns, 8 overflow). At the later pump, possibly with a religion +1 happy resource, it is (5 turns worker, 10 overflow) (8 turn settler, 12 overflow)
These are just sample cities that I personally got. With my Military and Capital producting units, and my Worker Pump pumping out workers and building beakers when growing, I quickly REXed 7 more cities, improved their strong points, set them into 'Provinces' and to continuing pumping units, military or otherwise, after basic city improvemetns. By 0 AD and some luck (Organized Imperalistic of the HRE

) I had 14 cities in Noble, of which 4 are Military Pumps, 2 are pumping workers, 3 are building wealth to help me recover with the rest developing. (Wow, I should make a REX Strategy Guide... Should I?)