For the wood, I would scrub it with 0000 steel wool and mineral spirits. It's just abrasive enough to remove the gunk and grime but not so much that it removes the entire finish. Once dry, finish with a hand rub of Tru-Oil which is just boiled linseed oil thinned with mineral spirits. It makes an ugly stock look pretty good.
For the metal, scrub it down with acetone and a stiff toothbrush. Cold Blue will fill in the light spots and blend fairly well. Understand that Cold Blue does not provide the same rust protection that real blueing does. It only makes the metal look darker.
If you go the Cold Blue route, you must apply some kind of protective product such as oil or wax to fight rust.
If you choose the rattle can approach, the metal prep is still important.
The old "once over dust, twice over rust" does not apply to firearms, only weather decks.
For the metal, scrub it down with acetone and a stiff toothbrush. Cold Blue will fill in the light spots and blend fairly well. Understand that Cold Blue does not provide the same rust protection that real blueing does. It only makes the metal look darker.
If you go the Cold Blue route, you must apply some kind of protective product such as oil or wax to fight rust.
If you choose the rattle can approach, the metal prep is still important.
The old "once over dust, twice over rust" does not apply to firearms, only weather decks.