Depends on the original finish.
If all it ever saw was wood oil, then that's all you should use. If it was finished using a varnish or polyurathane, then that's what you should use, respectively.
But be careful...you said "shine" up the stock, not "re-finish". To me, these are two entirely different levels of work and effort.
Shine up, to me, means "clean and polish". This means clean all dirt/debris off the stock and, essentially, buff it. You can buff by hand or with a buffer, either way. For an oiled stock finish, you can re-oil and buff.
Refinish is entirely different. This involves smooth-sanding the stock down, usually to the wood, to remove at least any excess or damaged finish. Personally, I'm of the opinion that if you re-finish, you should take the time to smooth-sand the entire stock because you'll likely want to re-stain the wood...or otherwise sand it until you get a uniform wood finish by removing all the existing finish.
Staining does a couple things: it gives the wood a color you like and it brings out the wood grain, both of which enhance the appearance. Oil based stains also add an extra layer of moisture protection to the wood.
The stock should then be re-finished using THIN coats of finish. A minimum of three coats, allowing plenty of time between coats for the finish to dry/cure (read the instructions for the finish you are using) and lightly sand between coats using a really fine sand paper. 400 to 600 grit is good for this. Just prior to the final finish coat, use 0000 steel wool.
The quality of your final finish is entirely dependent on your cleanliness and preparations which take place during the entire process, so don't skimp on this if refinishing is the route you decide to take.
The finish coats do a couple important things, too: they seal the wood against moisture and other contaminants, which protects the wood. They also enhance the appearance of the wood, as well.
I suspect, based on your question, that all you really want to do is clean it up and buff it out a little bit. Either way you go, however, do a little research online about this. There are a lot of products out there for this, for oil finished, varnished, and polyurathaned stocks. Choose a method and product which suits the existing finish on your gun, especially if you're just looking to maintain the original finish and just clean and buff it up. A complete refinish you could pretty much choose whatever you want to use and it wouldn't matter.
Which ever way, have fun with the project. There is great satisfaction in such a job when it's well done.
EDIT:
I'm not a big fan of "waxing" stocks, especially older stocks with original oil finish. It may look good, but it's kind of an apostasy to me to "violate" an original, possibly antique, finish by slathering on coats of wax. I'm more of a "restoration" kinda guy. Either restore/repair the original finish, or refinish it entirely by some method commensurate with the period methods in which it was originally built.
But that's me.
