If the current owner has any scruples, he or she will allow you to have it checked by a mechanic. Take it to someone you trust. If you don't know anyone in the area, ask around. Everyone worries about the condition of the engine and transmission. While these are important, due primarily to the expense involved to repair, they should not be your only consideration.
Brakes are very important also.
Now check the interior and exterior cosmetics. The appearance of the car. If there is any rust, or worse, perforations from rust in the body, your car could rust beyond repair in one winter. Oh, and those funny tubes and pipes under the car, the ones that carry gas from the tank to the engine and brake fluid around to all four wheels also rust. Bottom line, rust is bad but not fatal.