I would say the 44-77 was second, there are reasons for my answer. the greastest number of buffalo killed for hides only were killed in southwestern Nebraska, western Kansas and northern Texas from the start of the "Great Hunt" in the spring of 1872 when the market for raw hides opened up to about 1877 when most of the Southern Herd was destroyed. The two most popular callibers were 50-70 and 44-77 with the 45-90 coming in third. The 45's did not come into the line till 1876 according to Frank Barnes.
So most of the southern herd was gone by then. The 44-77 was considered light by some and most used a 50 cal if they could get their hands one one. Also the ammo given to the hunters by the army was of the 50-70 type, the 45-70 coming in in 1873 and most was needed to build up stock, the 50-70 was phased out and was less useful to the army. Also loose powder and stocks of Minne balls were also given away, left over from the Springfield muzzle-loaders. There is no offical records of the ammo give away, only accounts by hunters of being offered this, perhaps another Goverment Conspiracy for those who like such stuff.
Also many hunters early in the careers used the 50-70 Trapdoor, called a needle gun by many hunters. The older models such as the conversions from 1863 Springfiels were sold cheap on the frontier as the newer models came out.
These are the reasons I say the 50-70 killed the most buffalo for hides. One could also use the free 50-70 ammo in a 50-90 if desired.
As for a begaining BPRC a 45-70 is the best choice, brass is cheap, dies are cheap, recoil is tolerable for most who have no shoulder problems and it will do any thing that is needed.