You don't need one unit per city early and mid game in civ. Unless your empire is small or you set Barbarians to insane. Initially have a couple of fast units to hold back the hoards but don't actually build an army until you run into some one else. Also unless your trapped, early game war is very counter productive. You are better off with peace for a while until more mobile forms of warfare comes along.
IN A.C. you really do need one unit per city, if just to fight off the mind worms, or if your the appropriate faction, capture them. Once you out tech everyone, you can pretty much conquer at will limited by logistics and support penalties. Eventually you have to stop due to pressure on your economy.
Oh, I love putting those God believing heathens to the fire. It is impressive just how many units they can throw at you. Even with the tech advantage, they can give put up quite a fight.
Be sure to have some allies and if you go to war, be sure you have some sort of objective to it, whether it is a limited war or total. One of the worse things you can do is over extent yourself regardless of tech. In late game, the A.I. will pull a 6 day war by nuking their own territory. By that time, they only want to kill as many people they can before they go down.