I've done this three times (for myself, for my mom, and my sister - though technically she bought hers with her own money).
A $3,600 Chevy Monte Carlo I had inspected by a 3rd party. A $5,200 Volvo that ran perfectly over three test drives. And a $5,600 Corolla with relatively low miles (100k) that was in mint condition.
Oh! And I had a friend who bought a $7,000 Civic that had high miles but was only like 4 years old.
All of them. Every single one. Had a repair that was $300-$400+ every other month or so, for the whole time of ownership.
Timing belts, serpentine belts, alternators, transmissions, AC, electrical (lights), etc.
I'm a firm believe in buying a $12-$15k certified preowned Honda or Toyota with some warranty, and sucking up the car payment, versus buying dirt cheap and old any day of the week.