With that budget you can get something decent if you aim for brands that have a reputation for lasting. Toyota and Honda are practically essential in this conversation because people keep buying them used specifically because they don't die. A Corolla or Civic from 10-15 years ago can run perfectly fine if they've had basic maintenance done. Nissan falls into that category too, though I personally have seen their automatic transmissions sometimes be a problem, so if you go with Nissan better look for a manual. Hyundai and Kia from more recent generations also hold up pretty well and sometimes you can get better features for less money in that price range.
What you really have to check before closing any deal is the maintenance history. Ask if it has its services up to date, if the transmission shifts smoothly, what the engine sounds like when it starts. Getting it checked by a trusted mechanic before you buy saves you from headaches later. Cars that people maintain well cost a bit more but it's worth every dollar, because a car that needs work every week ends up being way more expensive than paying a bit more upfront.
Avoid the newest stuff from sketchy brands or models that come out of the factory with problems. With 8-10 thousand dollars you don't need the latest, you need something that works. A 12-15 year old car in good condition is going to give you way more peace of mind than a newer one but with a pile of repairs waiting to happen.