First, unless you’re really good with cars do make sure that you have a trustworthy local mechanic who can give cars the once over for you.
I would be combing your closest craigslist (or 2) for any of a number of small compact cars such as Saturn S series, Chevy Cavaliers, Chevy Prism (likely a very good bet), Ford Escort/focus. These can easily be had for anywhere from $2-4K in something like the '99-03 year range with something in the neighborhood of 100-120K miles on them. If well-maintained these cars tend to be reliable and easy to maintain - and if maintained will usually have another easy 100K in them (at least) with mostly normal wear and tear repairs.
The important thing is to get a good mechanic to look it over and to know something (preferably in writing) about the maintenance history.