Well, my friends and I are playing cooperatively against computers in locked alliances on Monarch level on a small map. That means that as soon as we have contact, we are instantly at war with 6 Civs and they are all friendly toward each other. In other words: we have 6 civs coming hard at us while we only have 1-2 cities.
It is a constant war game, always at war, no break. So from the get go I am cranking barracks and units. I generally dont even have time for a temple until later on. I try to get a granary or two, but sometimes time does not allow for that.
Basically it is [barracks, troops, settler, troops] for each city that I build until I get about 7 cities. If I have made it to that point, then I can worry about infrastructure. =)
Verax