Does anyone have any tips on buying a used car?

My husband got into an accident a few weeks ago and thankfully wasn’t hurt. The car however, is totaled. We have been driving a rental for 3 weeks, and just got the check from the insurance company. We have about $8,000 to spend on a used car. We have searched several companies online, such as carmax, veehix, auto trader, et cetera. We are pretty wary of private sellers, as we don’t want to end up with a shady situation (such as owing money on a title). I am wondering if anyone has any tips or sites to share, time-saving advice, or anything that could help us on our search. Thanks in advance.