Great to hear that a your son has an interest in old cars. These cars suck up money very quickly so be careful. This might be a good order of priority for him. These things don't cost a lot of money to start with.
Make the car safe. If tires are older than 7 years (check the DOT date on the tire) replace them. Check all the brake components including the parking brake. Check the suspension parts especially the ball joints and steering linkage. Check the throttle linkages and throttle return spring. Visually check the wiring for obvious frayed wires on loose connections. Check that all lights work.
Make it reliable. Visual all the hoses, belts, spark plug wires. Check the engine vacuum at idle to be sure it's steady and about 15-17 in. Hg. check all the fluids. Trans fluid should be red, clear and not smell burnt. Cooland should be clean and checked for level of protection against freezing. No evidence of radiator leaking Change the fuel filter. Spray clean the carb and change the air filter. Take the spark plugs out and visual them against a color chart that shows how the engine is performing (too rich/lean, burns oil, timing off, etc). Drive the car slowly in a figure 8 in a parking lot somewhere. If you hear a grinding feel or noise from either front wheel or hear a squeak, replace the wheel bearings.
Make it comfortable. Clean the interior and buff the paint and chrome as best you can. Check the shocks. If they look old, show signs of leaking or if the car continues to bounce after you rock the car up and down change the shocks. Check for water leaks from the seals and around the back glass (look in the trunk for signs of a leak).
Have fun. As you get some extra cash buy stuff that makes the car more personal like a modern audio system, new wheels, etc.
Use this forum for great help and advise from people who love these cars. Good luck.