Elizabeth,
Welcome to 150-152 club.
Three years ago when I decided to buy an airplane, I knew nothing about what to look for, so I found a mechanic that several people recommended, then he put me in touch with a experienced FBO and pilot who helped with the search -- I paid him some big bucks.
The first plane had damage history, the second one looked like a winner, but a title search showed a lien against it, the third appeared to have work done almost every week according to the log books. The plane was possessed by the devil, or so the owner frankly stated considering how it never seemed to fly without work needing to be done. Finally we settled on a plane that happened to turn out to be an IFR equipped Cessna 150G former float plane with a 150 hp Lycoming 320 engine and a few other extras for a very reasonable price.
Some rules of thumb I think I would follow if I were buying any airplane. Take the simplest step first (looking at logbooks) and then proceed to the next step if it passes muster.
Find a mechanic you trust, be willing to pay him to look at the log books (these can be copies or scanned or photos of the pages) and if they are available other paperwork such as receipts for items installed on the plane.
Talk to other people about the plane such as its current mechanic or previous owner.
Arrange for a test flight. Would you and your passenger be comfortable flying in the plane? In my case, and my wife’s too, despite a poor interior and exterior we were impressed with the sound of the engine and the lack of vibration. The mechanic confirmed all compression was 74/80 or better (and then explained to me that that was good.) My mechanic, not the owner’s, did a full annual inspection as a condition of the purchase.
Ask yourself your primary purpose or use of the plane and can it do what you want it to do?
Here is something a lot of people do not realize. The answer to the question “Did you get a good deal” cannot be answered until you have flown the plane for several years. If it requires a minimum of work and doesn’t let you down, then you got a good deal, even if you paid three or four thousand more than a similar airplane. If it requires a lot of work or you find yourself uncomfortable flying over areas without emergency landing sites, then it was not a good deal even if it cost three or four thousand less than a similar airplane.