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As said before Civic or Corolla are your best bet. For under $3K it will be a mid-90s beater with 100K+ miles most likely. These are popular cars so they keep their prices quite well. You can look at Nissan Sentra and Mazda Protege too. Being less popular you can find one of those with lower mileage at this price. Another one is an older Subaru Impreza but those are fairly esoteric so some research is required prior to purchase. Avoid Mitsubishi, anything German or American.

Don't expect a $2500K car to be trouble- and maintenance-free. You'll most likely need to do some maintenance and some fixing on it especially if you plan to rack up miles on it.
 
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