I would suggest using a finish remover to minimize the risk of sanding off too much wood. You want to be very careful about sanding inside the action area so that you don't change any critical dimensions.
You don't have to get fancy with any mixtures. Boiled linseed oil comes with drivers already mixed in. You will want to thin it down for the first coat with a 1:1 mixture of paint thinner so that it soaks into the wood better.
Circa 1850 Tung Oil is also a very good product and it doesn't have to be thinned.
You will need to decide how you want to fill in the wood grain, either with a liquid grain filler (not wood putty) or by repeatedly wet sanding the oil into the wood with fine grit sandpaper (like 320, 400 or 600 grit). This takes time but I enjoy the process. The wood dust and oil finish mixture gradually fills and levels out the pores.
Boiled linseed oil and (real) tung oil finishes are nice because they soak into the wood and aren't tacky like varnishes which sit on the wood.
However, they require multiple applications (24 hours between applications for drying) to achieve that satin matt look. I did 10 coats.
Let the last coat dry for a week, buff the stock and then finish with a good quality paste wax.
iirc, the old military rifles were just finished in either boiled linseed oil or tung oil (just dunked and soaked in it then wiped off) as it was cheap and simple. The oil dries to semi hard substance in air and sunlight over time, which seals the wood to protect it. The stocks would be oiled routinely (annually?) after that to maintain the finish.