Yeah, the amount of money you can spend is really important. Personally I would recommend anything you can afford to buy outright - getting in debt sucks. And a car with 50,000 miles on it costs a lot less than one with 0 miles on it, yet it will last nearly as long.
I am partial to Japanese cars myself, but American cars are less expensive and have been getting steadily more reliable over the years. As an example, my parents recently bought a 1996 Honda Accord, 4 door manual with about 130k miles on it, for $4800. Meanwhile, a friend of mine bought a 1993 Buick Park Avenue with 160k miles for $2000. Granted, the Buick was a few years older and had a few more miles on it, but that's a major difference in price.
Corollas and Civics are good small cars and they shouldn't be too expensive if you get a 3-6 year old one used. They should easily last past 200k miles, probably past 250k if you take good care of them.
POST EDIT: Just noticed your response after I posted mine. I was going to add that you could even go the route some people I know go - one family friend is a well-to-do bank president who buys factory reconditioned Lexuses at around 100k miles for something on the order of $20k. He drives them until they hit 250k miles and then sells them for a few thousand bucks to a not so wealthy friend of mine who drives them for yet another 100k miles. Lexus makes probably the most reliable cars you can buy so keep that in mind. A Lexus with 150k+ miles on it might be pretty expensive given how old it is, but there's a good chance it'll last just as long as a small car that you buy at 50-75k miles.
Given your price range, though, it might be fun to just buy a brand new car.
