Care/cleaning of old finish
 

I picked up a cheap 1950's archtop to mess around with, and the finish is definitely showing its age. There's a fair bit of wear, and some scratches above the strings where someone was a little too enthusiastic with upstrokes.

I'm fine with how it looks and don't want to refinish or anything, but is there a polish or product I can use to protect and clean the finish?

I use some of Mothers' automotive cleaners and polishes. I don't have the names with me, but their product line includes some very, very fine cleaners and a truly excellent, very light carnauba polish. I hate wax and buildup, and this stuff leaves virtually no product on the surface. For a really worn finish, it is possible to do a quick, minimal French Polish and restore beauty without any real buildup and while maintaining the vintage wear. Dan Erlewine mentioned this casually in one of his videos and I tried it on a really old, worn, beautiful Gibson and it restored depth to the sunburst and luster everywhere without any of that oversprayed, refinished look. I was astounded. Good luck getting yours spiffed up. I really love the look of an old, played, but clean guitar!

Stew-Mac shows how to use amalgamator to melt out scratches in old finishes in this video:

https://www.youtube.com/watch?v=FISY9I6pQdQ

Mamie Minch. who demonstrates the process, is an artist with this technique; she erases scratches so well that the finish looks like it's never been cracked.