You do not have to remove all of the old finish, just lightly sand it with about 400 grit to give the new finish something to bite into.
I like Ace Hardware's spray poluyurethane and it comes in gloss, satin or flat. Make sure what you use has UV resistant properties.
Wipe down with alcohol to remove any residual oil and spray a light coat, and let it dry overnight, then hit it with a slightly heaver coat the next day.
Continue until you get the coverage you like.
If you have dents you can steam them out with an iorn and some damp cloth. You can touch up chipped and light spots with a bit of oil stain.
Be sure to seal the butt, stock hole, and pistol grip where it mates with the reciever.
I spray a bit in the lid of the spray can and apply with a cotton swab or small brush. Do this before you spray it.
Post a picture if you need more advice.
Remington uses a synthertic finish now days, probably and epoxy or polyurethane.