Brass sounds good. Bronze wool used to be available at grocery/hardware stores, now mostly replaced by Chinese stuff. However you CAN get bronze wool thru internet. Brass/bronze & some simple penetrating oil, the hateful WD-40 if you must, perhaps better Kroil.
As far as a finish/preservative for the wood, if it is available at a good grocery store or hardware I would consider it poison & not let it touch any antique wood. I'd leave the wood alone. Wipe off the dirt with a rag lightly moistened with something simple, like vinegar, or at most real distilled turpentine.
Johnson's Paste wax would be a good thing to apply to the barrel once you've scrubbed it to your satisfaction. Would suggest you just remove the loose rust, leave the thing brown.
Museum types say use a "microcrystalline wax", which Johnson's Paste wax is. But it may no longer be commonly available, having been replaced by something with silicone.
Do not use silicone containing anything. The film will preclude you or anyone else using a different finish, such as cold pressed linseed oil. ever in the future.
I'm told that Reniassance Wax is state of the art for protecting fine antique metal stuff, such as armor.
Over the years I have seen more damage done to antique arms by collectors Improving them than by age & neglect. This includes even well respected dealers, scraping off patina so the markings can be better read in a photo.