To Quote Mike Venturino "ALWAYS GET THE .45-70 FIRST!"
For smokeless, the others are a waste. For BP, it will teach you everything you WILL need to learn in order to load the others with any semblance of accuracy. You can always ream out, you can't ream back.
.45-70=common components, easy to load, best to learn on, just enough power enough for anything on the NA continent, factory loadings available.
.45-90=developed as a target cartridge, excellent for LONG range target shooting, trickier to load, more expense. Not for a beginner.
.45-110=the ultimate, definitive Sharps .45 buffalo cartridge, long range killer of the Northern herd. Advanced loading techniques, recoil suitable only for heavy barrel rifles, Very expensive brass. If I was actually going Buffalo hunting, this is the one I'd want for BP. Too much for anything else. (Needless to say, I have one, and I'm hauling it to the Nebraska Sand hills one of these days. But I had a .45-70 first, and still do.)
.45-120=an historical chimera, never chambered by the Sharps rifle co. Developed by Winchester long after the buffalo were gone. Near impossible to load to fine accuracy, suitable only for those who just have to have a torpedo on their cartridge belt.
IMHO.