It can depend on what you want for the "finished" piece. Restore is to bring it to the "as found" condition, renovate means make it like it was new. Maybe only to just remove most of the dust/gunk/grime from the stock & metal parts, or something more. Do you care if whatever you do is reversible, so you can get back to the original condition, minus any duct/gunk/grime you removed?
Most museum restorers start on wood with the most benign and reversible process: water on a rag. Then soapy water on a rag, then a solvent like alcohol/water gently wiped, maybe then try acetone, then lacquer thinner, etc. And note that museums only want to stabilize the item, not make it useable for its intended purpose. It should be presentable for display in its "as found" condition.
Rust on metal presents another problem: rust and the resulting pits on the surface. You can't make the pits go away, but you can clean the surface rust by rubbing with a cloth with any of the several modern rust-dissolving solvents like Kroil , PB Blaster, EVAPO-RUST ... Then follow-up with a surface wax that can be removed, like Renaissance Wax, and will not react with either the wood or metal.
If your goal is to return the firearm to the original, factory-new appearance, you'll need abrasives and carefull work, but know that you are removing original metal to get out the pitting from the metal, and wood around gouges and nicks (there are a few tricks, most imperfect, to raise dents in wood), and not reversible.