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?

That would be pre 1982 except for 1943 zinc coated steel. Our copper pennies (pre 1982) are actually bronze (95% copper and 5% zinc). If you can't read the little date numbers the pre 1982 ones will "ring" if dropped on a hard surface like marble or granite kitchen tops or even formica and the 1982 plus ones will "klunk". If we use up a lot of the pre 82 ones we can drive up the value and that is my 2 cents worth.

You guys have a lot higher class rifles than I do.  A wire wheel on my grinder takes off the lighter rust, I have a 2" belt grinder with fine belts to take off the worst.  Any kind of motor oil will do when I'm done, used from my truck is cheaper than buying Kroil or ATF!