Finish the inletting. Then seal the inletting and all the interior of the stock with Tru-Oil. Remember to deal with the end-grain on the buttstock and on the fore-end. You might want to spray some sort of spray varnish into the two large hole drilled in the buttstock as that will help deal with any possible entry point for moisture.
If you want a USGI type result, then limit the degree of sanding you do to the wood. Look at some USGI wood, especially pictures of the Correct Grade and Collector Grade M-1 rifles being sold by the CMP. As the wood on these rifles is original, you can see the degree of sanding given at the arsenal. You can also judge the color of the wood. If you want a USGI type finish, you can use Tung Oil, rubbed on by hand. Until the early years of WWII, tung oil was the standard arsenal finish. Boiled Linseed Oil was made available in the field for maintaining the finish. Tung Oil w/o additives will give a very good finish. You might then want to use a little Gunny Paste rubbed on with the heel of your hand. It gives a beautiful luster and the smell is wonderful. If you wish to have a more protective finish, use the Tru-Oil. I have had very good results applying it by hand sanding lightly between coats. Some folks use 4-0 steel wool. The only potential problem with that method is that odd bits of the steel get broken off and wind up in the finish. To cut down on the shine, rub the dried finish with either 4-0 steel wool.
Your rifle will turn out beautifully. When you are finished, be sure to put up pictures!