If it's in the shop for the cooling system, ask the mechanic to go over the car with you while it's on the lift and with the hood up. Knowledge is power.

Prioritize your questions. I recommend safety, then reliability, then comfort, then style.

For me safety means stopping and steering, so look at brakes and steering components. Reliability means the engine doesn't need to be coddled to get me from A to B and back to A. So you're looking at compression, valves, intake, fuel lines and tank, oil, etc. Comfort and style come later, but you can't ignore them. If the heat doesn't work or the seat springs poke you, then you won't want to drive the car.

Your current problem is the cooling system, but you also say the cooling system was worked on. Is the failure related to the previous repair, or a different component? Did a 40-year old rubber hose blow? A rusted radiator? I presume there was no overheating.