Looks like a nice example of an "Ohio rifle" which were popular in the midwest after the area was well settled (1830ish) to the adoption of cartridges. I'd expect it to be a small caliber, no bigger than .45 but more likely .32-.40. The big game was gone, they were for squirrels and other small game. It looks original. If you ever get to Medina go to the Log Cabin gun shop, they have a big collection of Ohio rifles.
Don't do anything other than wipe it down with oil, swab the bore. BTW make sure it's not loaded, a surprising number of old muzzleloaders are loaded LOL