I have the JC Higgins 31 with a Higgins brass and steel scope. Got it at the Reno Gun Show last year, fellow who sold it to me said it had only a few hundred rounds through it and I think he was right. Of course he failed to mention it was during the Eisenhower Administration and no one had cleaned it since. It was a PITA to clean out all the caked in grime, took about 2 hrs worth with Hoppes on the trigger group and frame.
I'd make certain it properly feeds and extracts and that the trigger system works properly. The claw type extractor used on some of these rifles can cost a few $$$. Numrich Arms carries most replacement parts and some are common to the 29, 30 and 31. You may have to replace the recoil spring, that's a cheap fix.
There's a rocker arm on the trigger group, make sure that snaps front & back. The trigger group is easily removed from the action by taking out one screw, you could ask to take a look inside.