Compression is checked with one of these.
Follow the directions that come with the kit. Basically it screws in place of the spark plugs and you spin the motor over with the starter. The cylinder pressure shows up on the gauge.
With an older heavy vehicle I wouldn't trust the engine to hold it on a hill. The only thing holding the car still is the friction and compression of the engine. If you think about it when cranking that is easily over come by a small electric motor. A stick shift doesn't have a parking pawl like an automatic does. Set the E brake. You would hate to have it end up at the bottom of the hill.
A one barrel carb is pretty easy to go through. A kit will come with all the soft parts. Pull the carb apart, spray every passage and hole with carb cleaner and an air hose and put it back together with the new gaskets. Watch out for small balls and springs in some of the passages. You don't want to blow them across the garage.