I'd look for some reference pictures of the arms in question; better yet if you can actually get to examine the piece in person, but then I'm one of those wacko gun nut types. Where are you in Florida? This being the Gunshine State, you can probably find a real live specimen somewhere close, maybe I can point you in the right direction?
Most "wood" colored paints are too light (Testor's Wood, for example); most military small arms with wooden stocks were finished with oil and/or cosmoline ( a heavy grease used to protect wood and metal for long-term storage), which causes the wood to get a lot darker. I'd start with a dark matte brown with maybe a little bit of a reddish tinge, then dry-brush with a more tannish brown where wear would show (on an infantryman's weapon, that'd be just about everywhere). Wood grain probably won't be apparent on weapons in 54mm/1/35 or smaller, I wouldn't worry about replicating grain.
As far as the metal parts go, a lot of the time military small arms were "Parkerized," a chemical treatment that winds up being a dark gray to almost greenish color. Black is just too dark, especially given scale effects on color. You can replicate the wear normally seen on metal weapon parts with silver dry-brushing (but go easy!). For .30 and .50 aircraft mounted guns (which were usually better maintained from a cosmetic standpoint than weapons on the ground), nothing beats Humbrol Gunmetal, IMHO. You really are not likely to see a shiny blued finish anywhere near a combat zone, so don't use grampa's duck gun as a guide!
Bottom line: always check your references and try to replicate what you see.