Even a rustbucket can have lots of life in it. My first car was a '66, bought it in '73 with 43k miles on it. The doors were already eaten all the way through at the bottom - there was absolutely zero in the way of rustproofing in those days. But the engine and transmission were beasts. 3-speed automatic with the 289 V-8 and I beat many muscle cars off the line.*
So, go drive them. See how the engine responds. See how it sounds. Feel if the transmission shifts smoothly. Unless the car has been modded, it's going to have a carburetor. Remove the air filter and look inside the carburetor to see how clean it is and look for gummy deposits. Of course, get underneath and test the floorboards for soft spots. If the body looks nice - bring a good magnet with you - test every area of the doors, quarterpanels and fenders for plastic filler. I'm not saying don't buy a car that has substantial bodywork done to it, just adjust the price substantially.
Lastly, even a car in really good shape is going to have things go wrong with it. These cars are fairly easy to work on. I replaced the radiator, the water lines, brake lines, shoes and pads myself, and I wasn't any hotshot mechanic. The only thing I had someone else do was re-core the radiator - don't know if anyone still does that these days. If you don't think you are up to do these types of jobs yourself, I would steer clear of ANY classic model except one with a professional restoration.
Lastly, if you like everything you see after checking, take it to a professional mechanic and have them go over the car.
* If you know the old Foreigner song 'Rev On the Red Line' and the line, 'Cruisn' all night on Lake Avenue - it's a piece of cake if you know what to do.'
Well, Lou Gramm is from my hometown and I used to run against the big boys on Lake Ave. Never engaged in anything high-stakes where you would lose money or have to hand over your registration, like the song talked about - it was just a song that romanticized things a bit - it was more of a thing where a Corvette or Super-Bee or Olds 442 would pull up next to you at the light and you'd exchange glances, 'You wanna go?' and I would blow many of them away - for the first tenth of a mile. Then I was toast. But that car was quick. That 289 was a big motor in that light of a car.