Winchesters are well documented. Post the serial numbers and somebody will look up the years of manufacture.
Value depends HEAVILY on condition and any unusual features.
A standard model 92 .25-20 carbine is listed in the Blue Book at $995 with 60% of the original finish remaining.
A regular model 12 pump 16 gauge is listed there at $295 with 90% of the original finish remaining.
Nicer shape, unusual or special order features = more money; more wear and tear, refinish, or user alterations = lower value.
If Great Grandpa was a lawman or historical figure and you have documents or pictures to place him with that Winchester, that would be very good. But family legend and oral history don't count for much.
Tell us more, we can tell you more.