I strip stock for refinishing with Homer Formby's stripper.
For the new finish, whether refinishing a stock, or a new one, I use the Formby's Low Gloss Tung Oil.
You need to get it up to 600 Silicon Carbide paper, and use a very sligtly damped tack rag to remove all dust. Clean the stock and workbench as well as possible.
Pour some of the tung oil into a shallow dish, a mayo jar lid, whatever, and dip your fingers in and rub onto the wood well by hand.
(Edited to add) Finish inside the stock as well as outside. Any unfinished areas will allow gun oil to soak in and seep under the finished areas, making an unsightly stain. Also, this will make the wood more stable, fewer changes from humidity and temp changes. This is important for accuracy.
The first three or four coats will soak in completely. This is good, it is penetrating and hardening the wood. Allow minimum of 8-10 hours between coats.
After about 6 coats, sand lightly with 800 silicon carbide paper, tack rag it clean, and apply a few more coats.
Yes, this all takes a week or so to apply a good finish, but is well worth it.