I want to buy a (used) car. What kind should I look for?

I’m a college student looking to buy my first car. I don’t care about looks as much, but I want it to be dependable (eg not a money trap, constantly being fixed), get good gas mileage, and an automatic. I’d prefer no older than 15 years, but that’s more flexible. I’d like to spend between $1000 – $1500. Basically a “point A to point B” car, with point B occasionally being a few hundred miles away.

What makes and models should I be looking for? How do I check for problems before buying? Am I being realistic in my expectations? Where can I look to find a good deal, besides craigslist?