Proper cleaning never hurts old collectible firearms. Heavy cleaning can damage finish, and hurt the value though.

I usually remove the stocks and use a soft bristle brush like an old toothbrush to scrub all the metal parts wetting the brush with Hoppes No. 9. Then I use Murphy's on the wood with a soft rag to clean wood. I finish by wiping down the whole gun metal and wood with Old West Snake Oil. This usually makes a huge improvement on really dirty old guns.
If there's any minor rust needing to be addressed I mix ATF and acetone 50/50 and wet the rusty area, then address the worst using the edge of a penny to scrape off rust, and 4/0 steel wool wetted in the mixture for overall larger area. Then follow with the first steps I laid out.

What's a penny?