The stock on my Mauser project gives the appearance of having been left out in the rain. It had a nice finish on it, but there are parts of the fore-end where the grain is raised.

My goal is to end up with a deer rifle for the late season, a true Gefrierschrank-fillergewehr. It will also function as the camp's designated loaner. If you had to ask me a preference, I'd say I would like to see a Winchester Red color and a finish that is fairly weather resistant and easy to repair.

My question to y'all is how to proceed.

You mentioned a tight budget, I'd just sand it smooth and finish it with Formby's Tung Oil finish. Has some varnish in it so it's pretty durable and it's a easy to apply. Also easy to touch up WHEN it gets some hunting rash.

Should I be worried about what's already on there before proceeding?

No Formby's on hand, but I did find a can of Watco Danish Oil. Will that do?

You should strip it before putting something else on because incompatiblily could lead to the new finish blistering or not curing correctly.
Watco will do. It's thinner than Formby's as I recall. I used it on furniture, not on a gunstock. But it's easy to touch up. But it's also not all that weather resistant.

My favorite combination is from Brownells.
Pilkington Pre '64 Winchester Spirit Stain for that warm reddish look. And Permalyn finish. It's the toughest rub on finish I've ever seen.

Sand it down and refinish it. Wood is wood. Anything wood I have is glassed inside and a polyurethane varnish to seal it up, but all I care about is function...I'm not a purist.

Either that or Krylon Camo or better works just fine. Krylon clear is fine.

Clear Krylon on the metal keeps that Rostfroi as well.