I'm no expert on buffalo rifle lore, but I believe the "long" .45's (-110, -120, etc.) weren't produced untill rather late in the buffalo era, and then not in Sharps factory rifles. The most popular early cartridges were the .50-70 (the common military round of the late 1860's up till the introduction of the .45-70) and the .44-77, which I believe was the original Sharps chambering. The .50-90 was in there too. There is some debate as to whether the term "Sharps Big Fifty" referred to the .50-90 or the .50-70, but in either case, I'll admit a 600-grain, half-inch chunk of lead is plenty big, no matter how much powder is behind it.
"Buffalo Rifles of the Old West" is good reference book for the various calibers and chamberings available, as well as sights and various Sharps rifle models.
The advice you have received from the others is the same as what I got when I asked - The .45-70 is extremely versatile, whether you want to hunt or target shoot. Ammunition, reloading tools, components and load data is plentiful and cheap, and available nearly anywhere. If you later want more bang, you can easily have the chamber lengthened to 45-90 or longer.