Facebook seems to have the lowest cost cars, but it also seems to be the least successful way of contacting people. When I bought a car for my sister in April, I contacted (no exaggeration) 70+ sellers and heard back from about ten of them. And yes, I changed the default "Is it still available?" message to something demonstrating urgency e.g. "I have cash and would like to buy." But with persistence, I found her the right car through Marketplace. Really hate the FBook search interface though, it's total garbage.
I spend most of my time looking on CList and OfferUp.
Same! I recommend an old (2017-) Nissan Leaf. I got one for very cheap when gas was at a local peak, and now that's it's going down, I'm seeing even better deals. The low range can be a plus when it's a 16-year-old driver whom you have no interest in seeing drive out of the city. haha