I agree with what Alice and Mint have said.
The thing is, you have to be sure you're ready for this (and look beyond the "Gosh, it'll be cool!" thing to the bill-paying and neighbor-respecting thing).
Most importantly, in this talk when you're trying to tell your folks that you're a responsible adult, act like a responsible adult. There's nothing more pathetic (and I know, because I've been this pathetic) than trying to get your parents to see what a responsible, mature adult you are by pulling a temper tantrum that makes a 2-year-old look like an angel.
This is the first of many, many, many adult disagreements (assuming there'll be a disagreement... your parents may suprize you) you'll have to work through in a mature fashion. Speak clearly, compassionately (after all, you don't know what it's like to be a parent who wants the best for her child), and calmly, and then back up what you say by your actions. If you say you'll come home on weekends, come home on weekends. If you have a self-enforced curfew on school nights, be home by that time. If you say you won't party, or drink, or do drugs, don't do those things. In time, your parents will come to respect you as an adult.
Regardless, though, you're still their little girl, and you should be prepared for them to come at the situation from that angle.
Good luck!