Just to add my two cents worth -- back in the late '80s I did a tremendous amount of research on buffalo hunters and what it would take to set up a proper outfit. I've got every book mentioned here that was published at the time, plus quite a lot that haven't been mentioned. Needless to say, I love to research.
So based on several years of books, microfilm and microfiche, visiting the various sites, different museums, etc., the conclusion I came to was a # 3 Sharps with a #1 heavy barrel (11-12lb rifle) and military butt stock, plain wood, and a rear tang sight such as Grogan supplied a photo of. I think it might have been Billy Dixon who said he shot as many buffalo with this type of set-up as he did with his 16lb rifle. The .50-70 and .44-77 seems to be the earliest and most popular cartridges with the hunters, which opens up Kansas and Texas if you are into re-enacting the period.
For what it's worth, Frank Mayer's book is considered suspect by historians, and I never found any reference to the government supplying ammunition to buffalo hunters for the purpose of promoting the hide trade.
Also for what it's worth, I went with the above set-up, but in a .45-70, which made it a lot easier and cheaper to reload for. And I'd also add that I regretted the military butt, especially for older shoulders. It kicks more than a shotgun butt.
Again, just my two cents worth, but I hope it helps.