For your price range, you probably won't have to go the used route, although if you go certified pre-owned you can get a good deal on a nicer car. A couple of reliable hatchbacks that jump to mind are the Mazda 3, Toyota Prius C, Subaru Impreza or the Honda Fit. If you are really concerned about maintenance, you might be able to find something with a maintenance plan. I wouldn't probably recommend going with an extended warranty with the reliability of these cars, but it would give you peace of mind.
FYI - if you are a planning to run the car into the ground, it is worth noting that the Mazda, Honda and Subaru all have non-turbo normally aspirated engines, which is better for long term maintenance/high mileage. More and more companies are switching to Turbo motors which could cause issues at high mileage.