Thanks for all the advice so far. To clarify a few of the quesitons:

Yes, the current freewheel is a 7-speed Regina extra 12-21.
Yes, I should replace the chain in any case.
The rear derailer is an old Campagnolo. I forget which type. One of the more basic models from the 80s. It works and looks fine.

The other idea that I had is to maybe leave the Regina where it is and replace the crankset instead. It is a more basic part anyway and I think I could probably find a matching Campa crankset for the bike instead.

My Puch Mistral currently has a 42/52. What would I need to replace the 42 with in order to come to a similar ratio that I would have with a 42 on 28 combination?