A Consumer Reports Used Car Buyers’ Guide from the local bookstore won’t specifically identify cars in that price raneg, but it will give you a good idea of those models that have poor histories. It’ll help improve your odds.
Beyond that it’s maintenance, maintenance, and how well the car was treated. Any vehicle you consider should be thoroughly checked under the hood and under the chassis by a reputable independent mechanic.
One caveat: do not fall in love with anything. Do your homework on every possible selection.
Oh, and be sure to let all of your family and relatives know that you’re actively looking. They can be the best source of a reliable used car.