From my limited experience, your 12C is probably an octagonal barrel pump which shoots shorts, longs and LRs. It will most likely have a corncob forend and a cresent shaped inletted butt plate. I think most were built between 1925 and 1929. Condition is EVERTHING. A bad bore is the Devil's curse and pitting is typical. A total restoration will cost more than an excellent condition example is worth. If you are looking for a very well made .22 pump, do some research on a Winchester Model 61.
Yeah bad bores are the bane of Rem 12's. I have one that's been in the family since it was bought new in the 1930s, but the bore looks like two miles of bad road. The steel was susceptible to the corrosive primers of the day, even when kept clean. It's the shorter, straight grip, round barrel version (I think that's the 12-A, but the gun is buried in the back of the safe).
The 24" octagon barrel version is the least common, other than some gallery models in .22 Short only. Prices for guns with a lot of use are typically $250 to $600, depending on external and bore condition. Mint can go higher, but most of these guns were well used, as they were small game, plinking and target shooting workhorses.
If you were near me I'd be interested in it, but by the time shipping and FFL costs are added in, the costs simply don't justify messing with them. They're a simple gun and as such they make a good learning tool for restoration.
Possibly, depending on the local interest. You could at least start there and see if you get any nibbles. The blueing looks in the pic like it's turning to brown, but incandescent lighting can cause that effect. If the blueing is actually blue, then perhaps try $550 and drop if no interest.