When going for an early rush you basically build nothing but units, forget about growth or city improvements. You build a worker to hook up necessary resource and build units, chop if necessary. Early rush should start about 3000BC or even sooner if possible. You might try to play Huayna, Cyrus or Hatshepsut, they have good, cheap early UU's, just to get a grip on how early rush looks like. Avoid rush on Mansa, his UU keeps him out of trouble until maces or elephants, bastard
One more thing, starting techs will play major role early on, early axemen rush might not be a wise option for someone who starts without mining. Those who start with hunting would go for archery or animal husbandry. You can't afford to depend on warriors to hold off any attacks, so military improvent is a first step you take, not pottery or such, although you might want to try and grab an early religion if you start with mysticism.
Regarding city micromanagment, you might play occasional OCC game, you'll really learn how to manage your cities to a tiniest of detail.