Maintaining wood stock?

If it has a finish on it already, just keep it clean. Treat it like a nice piece of furniture. 
If it does not have a finish on it, there's a few different methods to put a finish on it, bring out the natural beauty, and protect the wood. Then, treat it like a nice piece of furniture.
Tom

Well its a little high but this is what I use and its used on high end wood pieces.

https://www.amazon.com/Renaissance-Wax-200ml/dp/B0012S1XBO

What I do with all my wood stocks is clean them with a damp towel dipped in Dawn detergent, mild mix. Then apply 3 coats of wood floor wax, paste, 24 hrs apart with a buff between coats. After that I just wipe the entire gun with a towel damp with Ballistol after each use to remove the fingerprints, yes metal and wood. Of course removing the stock before waxing is recommended..
Why Dawn? Because it removes any wax/oily residue left over from manufacturing or handling.
Why floor wax? It's tough enough to protect from shoes with lots of weight on them.
Ballistol will protect the rifle/pistol and remove fingerprints.
I have been doing this to my powder burners for many years before I got interested in Airguns.
This works for me, your mileage may vary.

I believe BSA use american black Walnut for their stocks - this can be quite dry.

I apply a light natural oil (like WALNUT OIL ) to my stocks - sometimes several treatments and I make sure the inletting also gets treated. It's my belief that this helps to waterproof the wood.

As a final 'coating' a high quality furniture wax will add a bit of lustre.

I have a walther from the 70s and the wood is still in mint condition. Nothing has ever been done to it. Its been shot quite a bit. 

I would use Oil.

I just wipe the entire gun, metal and wood, with Ballistol every time it is handled.

I agree with the use of Ballistol, have been using it for years on all rifles with great results-good stuff!