What's the most important thing I should save up for?

The most important thing is to be able to pay your bills, rent, gas. electricity, cable tv etc. You will also need gas money and maybe order an internet connection (another bill) where ever you will be renting. While you are a student, you can make friends and car pool and also save on food by eating together instead of cooking for 1 all the time and inevitably wasting food. Your family may still help out while you are a student so take what you can! All you should need when you move as long as it is furnished are your clothes, towels and sheets and your groceries, bathroom stuff and some cleaning stuff in the kitchen. Beg & borrow from friends and family as you start off people are only too happy to help if someone is looking for a second hand couch or table etc. You should consider renters insurance and make sure you have enough insurance on your moms car to carry pengers etc. Best of luck!