Prince difficulty, I generally attempt to rock a technological superiority as fast as possible. The way to do this is go straight for GL, it shouldn't be all that hard to get. If you want to play faithful, go for stonehenge, if you want to be naval, go lighthouse. That's my general policy.
I like to start with tradition to open straight off, then if you go with the wonder policy you can bang the ones you want out quickly.
The biggest economic downfall is trade routes. A surprising number of people think they're automatic economic benefit, when in reality there's a formula. You want to wait until the city you're connecting (capital only gives you a benefit when it gets to ~8 pop) is around 4 or more population. Since every road costs 1 per turn per section, you gotta do the math on which ones actually get you bonuses. The other economic thing you can do is shill off your early wonders for beautiful, beautiful cash. 1 luxury=optimally 240gp with a computer player. You can make up for that with gold per turn if the AIs are short on cash, just think of each gold per turn as 30gp. If the computer really does like you (this is a great way of checking how they really feel about you) they'll accept 240 gp.
Defending/Attacking: Hitting things up close is so last civ. Those ranged units are your best friends in the ancient/classic/medieval era, right up to cbows they're THE way to take on enemy civs on attack or defense. (after that, hop in a plane and grab some artillery or battleships) They hold out and whittle down enemies without taking any caualties, and 3-4 ranged units and a melee unit in the wings will bring down a city with minimal problems.
Happies: Happiness, besides the obvious exploring/luxes/buildings, religion is your friend. If you're focused on it and get the first one, THE BEST combo is Tithe and Pagodas. Tithe gets you money for nothing and pagodas get your kicks for free (ha! That worked better than I thought). pagodas are probably the best faith sink, tons of bonus happiness with no need for production or coin, and if you snagged an early religion there's really no need to fight to spread it, it'll just spread gradually on its own.