Hi!
I shot my first deer in Louisiana and my son was born there. I was a grad student at LSU at the time (Geaux Tigers! 2 losses in 6OT's
but I digress. . .)
I have refinished a fair number of stocks, so if I may, I would offer the following suggestions:
Polyurethane the interior of the stock with several thin coats. If you plan on refinishing the exterior, and in order to preserve the value of the gun, I would highly recommend stripping it with Homer Formsby. I would then fill the pores of the wood with French Red filler--this will give you the characteristic red color found on old Savages and Winchesters. Follow this with several (at least 5) coats of your favorite oil finish (Linspeed is OK). Use minimum 200 grit sand paper. When you're ready to take it into the palmetto swamps/piney bayous, rub a GENEROUS coat of Johnson's Paste Wax all over the gun. Reapply during the season as necessary. When the season is over, buff the wood to a nice shine. If you get a bit of oxidation from the wax, Murphy's Oil Soap will clean it up.
I know the above is a lot of work, but you will have a nice, water-proof stock with an apparent original finish.