I also advise staying at home as long as you can manage to knock out those loans. It gives you a great flexibility to leave when you want.
As far as your parents charging you rent, I'll just mention what my plan sort of is for when my kids get older. We have a property that works very well for multiple adults living here and having some independence, and so I expect this may happen. And in fact, I'd like for it to happen, both because we all get along well and because it would help my kids achieve their financial goals. My plan is that once they're in the "real world," (after college or when working), they will pay a proportion of all household expenses. Now, my spouse and I pay 100% of utilities, food, property tax, etc., but if we have one working adult join us, that person would pay 1/3 of household expenses. If a fourth or fifth (through a roommate situation or significant other) joins in, that reduces everyone's expenses proportionately. And it isn't because we "need" the money, but it is what's fair. That $600/month means your parents can take a few awesome trips every year, all while helping you out. Or it means they'll be able to pay for longterm care insurance, or...whatever. I do think it's fair, and I think keeping money in the family is a good thing, too.
But it also means you are an equal partner in the household, and the negative aspects of "parenting" should stop.