I bought my first car from a private seller as well since then I do trust dealerships only. As a rule they don't sell bad history cars and give some guarantees. If you've already made up your mind at least take it to independent mechanic. Or lookup car by vin: https://trustvin.com/auto-history-by-checking-the-vin-number there are lots of other alternatives like autodna.com, clearvin.com, nadaguides.com Choose what you like, compare prices.
Still I strongly recommend not to buy from a private seller!!!