I'm not going to preach the "best" way but I'll tell you what I've learned restoring a couple stocks.
Home hardware has all kinds of wood finishes for restoring antique furniture. I acquired circa 1850 stripper there - soaks up any old stain, removes old oil, safe on the hands, non flammable. Follow that up with steaming for dents/dings stubborn stains.
Boiled linseed oil is the way to go on a military stock unless you have a million years to wait. I thinned mine 50/50 with mineral spirits to speed absorption and promote levelling of the finish. Helps it dry quicker as well.
And when I say quicker, I mean, cuts drying time from 48hrs+ to a more reasonable 24ish.
If you want a quicker more gloss finish try something like Tru-oil, which is also linseed based but more modified. Dries in about 2 hrs with a high gloss.
Buff between coats with scotchbrite pads-- stay away from steel wool. It leaves tiny particles everywhere and embeds itself in the wood. I hate the stuff.
There's my 2 cents. Should be a fun project - be sure to post pictures as you go along, they're fun to see
