In harder difficulties, the only way to defeat your enemies is military and a lot of luck. No matter what you do you can't research faster then them, and the most wonders you can build first is probably 2. Assuming you don't cheat and give yourself gold, wine, and fishes on every tile. ;D
In monarch and below, it ain't difficult. Just spam a lot of cities and workers early and make smart trades. Also get into money-making governments only. Beeline for aqueducts and hospitals for supersize cities. It ain't hard to get all the wonders either. Pyramids is probably the most important wonder.
Also, in cities with too much corruption, farm all tiles, because only those specialists will do anything. xD
I like egypt for their worker's speed and the cheap happiness buildings, plus no unpredictably long anarchy. And of course, war chariot. Cheap and deadly.