Whether buying from dealer or person, I would not trust them for the history of the car. Usually when buying from dealerships, you can ask them for the car fax report for the car free of charge. They have those on hand to show potential customers. People selling their cars aren’t required to do so. So ask them for the VIN# of the car and go to carfax and pay the money to find out the car history. You’ll be glad you did. When my dad shopped around for a car, he got a carfax account for a month, in which time you can get reports for unlimited VIN#s. So when you get your account, be sure you have looked at a bunch of cars and know their #.
Personally, I prefer buying from people vs. dealership because people aren’t trained to be sleazy douche salesmen/women. Once I meet the person and talk to them, I can pretty much tell if they are being honest or if they are trying to hide something. But the dealership do give warranty, which is a big plus. In addition, paying the dealership can be more flexible than a single person. Dealerships offer installments etc, which you can also arrange with the bank while buying from a single person, but it could be more complicated.
As long as you buy a dependable car like Honda/Toyota, that is not too old, you should be fine. My dad is a pro at shopping for cars so I will ask him tonight if he has anything to add.