If you want the wood to match, you'll have to re-finish the whole thing. However, wood is wood. You use the same techniques and products used on fine funiture.
You have several options as to what finish to use. Birchwood Casey Tru-oil is likely the best for your purpose. Your local gun shop should have a kit that includes instructions.
Or you can strip the finish and apply Tung Oil. It takes longer(several coats get rubbed in over several days using a clean lint free cloth/rag and let each coat dry for 24 hours. Brings out the wood grain very nicely.), but gives you a hard, waterproof, finish. The more you rub in, the shinier the finish. Any stain must be applied before any tung oil is applied though. Once the oil is on, there's no going back to stain. Tung oil(Pure tung oil. Not a tung oil finish.) can be found in any hardware or paint shop. It's not exactly cheap though. Runs about $15 per litre. A litre is plenty. A little goes a very long way.
The other option is Boiled Linseed Oil. AKA BLO. (Boiled or double boiled, not raw. Raw linseed oil doesn't dry.) It's the finish seen on most W.W. II rifles. It gives a flat finish. Strip the wood and apply it with a clean lint free cloth/rag. 24 hours between coats too, but you don't need as many as tung oil. The only scary part of BLO is that the used rags must be disposed of in a safe place. BLO soaked rags have been known to spontaneously combust. Even dry rags. Tung oil doesn't. BLO will likely be next to the tung oil or very nearby.
The advantage of either oil finish is that if you should scratch the stock, a bit more oil rubbed in will make it go away. That doesn't happen with plastic polyurethane finishes. Polyurethane belongs on cheap furniture, not gun stocks.
Another option is to strip the wood and apply Spar varnish. Haven't used that myself though. Hardware store or marine supply shop.
