a few g's would be ideal but realistically 1500-2000 is going to cover most folks first and last, who live in studios.
if you can save more, do it. you dont want to work check to check to pay your rent off, trust me.
also look into a credit card with a 800 dollar cash advance or something and pay your rent off monthly with the credit card, so you can build some credit. if you have anyone who trusts you, have them cosign for you. but if you go that route, NEVER DO IT IF YOU ARENT 100% SURE YOU CANT PAY IT OFF, QUICK.
youll hear many horror stories about that.
possibly look into college and get grants/financial aid/scolorships. that might help you rent or get you free dorm.