If I can make a suggestion: I’d say to give the watch a proper service and exterior clean, maybe replace the crystal and strap, but otherwise leave it as that. The dial you not going to improve (without ruining it further) and the wear marks should remain. Going for a full polish will be going too far as it’ll lose all the wear that your grand dad has put there. It’s then not your grand dad’s watch, but some random old watch from the 60’s with a beat up dial. Finding parts in good cosmetic condition ain’t gonna happen, so you can only go so far anyway
We actually had a long chat about this very thing in the Horology thread. Anyway, it’s a very personal decision of course, one that only you can make. While I restore most of the ‘junk’ watches I come across, I have no sentimental connection with any of them as it’s something random I came across at some pawn shop. When it’s a sentimental piece, things change: you want to get it working reliably and clean it so you can use it. But with polishing it up you stand the chance of making it worse. It’s a delicate thing with such pieces.