I suggest that you don't refinish it. This is how I would do it and it would keep the patina that makes it beautiful. A newly refinished stock will diminish the years of love and use that it's had. The tone and feel of aged wood can't be duplicated by refinished wood.
Dismount the stock and forearm and clean them with some #0 steel wool and linseed oil. Finish up with #0000 steel wool. Just rub with the grain and go easy. All the dirt should remove quite well. Then, just apply a coat or two of paste wax and buff it to a dull sheen.
Any dings or scratches will fill in a bit and they give it some of its character anyway.
“If ye love wealth better than liberty, the tranquility of servitude better than the animating contest of freedom, go home from us in peace. We ask not your counsels or arms. Crouch down and lick the hands which feed you. May your chains set lightly upon you, and may posterity forget that ye were our countrymen.” ― Samuel Adams