All I can say is that I have regretted every private used-car purchase I have made. They all had multiple problems, including one that I bought in winter that overheated in summer.
Granted, these purchases were at times when I was short of funds and had to fish in the shallow end of the pond.
I try to pay cash whenever possible, but older cars (5 years or so) are generally in quite good shape these days. Reputable dealers don't keep junkers on their lot, and you can get decent financing from a credit union.
You might also try an auction, where at least you know you won't be stuck up. However, you had better know what you're looking for and at. Auctions are as-is-where-is with no warranty.
- Jim