You've got a really good neighbor. Winchester .22s are my passion and addiction. .22 extra longs were their own cartridge. 1902s, 1904s and some Thumb triggers were chambered for S, L, and extra longs. The later 1904s were reclassified as model 04s. The 04s had a regular shot gun style butt plate, not the classy crescent butt plate like the early 1904s.
I always thought the 1904s were one of the prettiest single shot rifles with the metal butt plate and the schnable forearm.
I would just use a good bore cleaner like Butch's Bore shine or Hoppe's #9 and keep working on it. You can clean the metal with a Frontier 45 pad or 0000 steel wool and a lot of oil. I would try something like Formby's furniture cleaner on the stock.
I wouldn't try to polish it to far, better just well cleaned.
You're going to love it.