I vote that you spend some time shopping used options. If no good deals are on CraigsList, then check local classifieds. A college town should almost always have something for a good deal. Also try garage sales and pawn shops.

For that short of a distance, pretty much any bike (mountian, hybird, road, cross) that is your size would work fine. If you do find a used bike that needs a bit of work, take it to the local shop for a tune-up. Then get a book or spend some time on YouTube watching repair videos. It's not that hard to learn basic bike maintenance. Much easier than a car.

After you've ridden a clunker for a while you will learn more about what you like and don't like and what may work for you long-term. Or you may also learn that cycling isn't for you, without having invested too much.

If nothing else, it can't hurt to have looked around only to learn that your best option is a new bike.