I guess it would depend on several things: What era am I portraying? If it is any time between 1860 and 1873, I guess I would opt for a M1860 Colt's Army, possibly with a cartridge conversion. For a long arm, it would depend on what I expected to encounter...large four-legged critters, including griz, I'd opt for a large bore breachloader. Yes, a Sharps carbine would seem to be the choice, but, frankly, I think I'd rather have a 5th Model Burnside carbine, with brass cartridge cases that seal the breach! If I was more worried about two-legged varmints, then a M1860 Henry Repeating rifle in .44 rimfire (presuming we are talking about what was really available), although a M1860 Spencer Repeating Carbine would also serve well for both big game and bad guys.
Now if we are talking after 1873, I'd switch to a Colt's Single Action and probably keep the Spencer until 1878, when I'd switch to a .44-40 Colt's and Winchester '73. After 1886, I'd go with a .45 Colts and a M1886 Winchester in .45-70.