Here is my own best used cars under $10,000:
Toyota ECHO any year
Toyota Yaris any year
Mazda Miata any year
If the car runs and drives, starts and stops, and has nothing obviously wrong with it and you have no reason not to like it BUY IT!
If the car needs work dont let that put you off. If you can do it GREAT! If you have a friend who can do it GOOD. If you have a trusted mechanic who can do it OK.
If there IS obviously something wrong offer less money. Dont feel guilty. Remember as my father said "The whole world is (blank) you and hurray for me!"
Remember the ECHO I bought for my son for $3000 six years ago with 117k on it. I would say we put $300 in it all in all. We sold it for about half that after putting ~200k miles on it. He drove to it Seattle TWICE with his gf. While we changed the oil fairly regularly, there were times when I checked the dipstick and there was NO OIL on it. There were times when we changed the oil together and 2 or 3 quarts came out. There were times when there was 10 psi in the tires.
Oh I forgot it needed a new MAF sensor but it took two years to figure that out. I discovered the problem when I swapped MAF sensors with my 09 Yaris. My CEL went on, his went out. Rebuilt MAF: $90 at NAPA. Its in my Yaris now. Mine is on its was to Costa Rice with the car.
BTW the engine and transmission were good on that car. He complained of steering issues. If we didnt have the money to get him another car I would have 1)fixed the car myself were I able 2) taken it to a trusted mechanc and said "Heres $2000 evaluate the car and fix what you think needs fixing $2000 worth. Call me and tell me what you find out and what you think should be done."
Then I would drive the car another 200,000 k miles!