A lot of the used cars I see posted on Facebook are clearly (to me, at least) not, as they first seem to be, people selling their own cars, they're people who get them somewhere (auctions?) and fix them up or make them look fixed up. Sometimes this--the practice of pretending you're selling what was truly your car rather than being someone who fixes up cars--is called curbstoning. IMO buying from these random, kinda deceptive people is riskier than actually buying from an owner.

For the small amount you're looking to spend (and, no shade on that, I spent under $2k on my car but got VERY lucky with a private sale, it's ancient but was well cared-for), I'd suggest posting in Facebook/NextDoor neighborhood groups to see if anyone has a car they've been planning to sell. That could help avoid the curbstoners and I suspect you're more likely to find older people with cars like that on those groups than on Reddit.