Look for a older clean Camry 4 cyl.
Yes very possible. I see Honda's and Toyotas on Craigslist all the time.
That'd be my list as well (but with Volvo thrown in). I've had great luck with Honda, Toyota, and Nissan (in that order).To get to that price point, mileage has to be really high. With that prerequisite, I'm sorry to say it, but import brands are the only option.
Subaru, Honda, Toyota, Mazda, maybe Nissan (don't know them that well).