I suggest reading Pondoro Taylor's writing, he was a trident admirer of the 375 H&H, my experience has been similar. I would suggest the 375 is the best "all around African caliber", but for stopping power with DG, I would yield the 400+ calibers are better suited. I would love to hear from those who have "stopped DG" with the 375 H&H.
Edward, take my quibbles here with the knowledge that they are, perhaps, inspired by a decent glass of brandy: I haven't stopped a Cape Buffalo in many years, though I'm a devotee of the .375 H&H mainly as a stopper for big bears, for backing up friends who hunt deer and elk in the wrong regions, as the smell of fresh elk gets into the wind (and I use 350 grain Weldcores for that bit, which I hoard).
I'll paste in this bit of Pondoro's writing about Holland's .375:
"Undoubtedly one of the deadliest weapons in existence. I've had five of these rifles—two doubles and three magazines—and have fired more than 5,000 rounds of .375 Magnum ammunition at game. One of them accounted for more than 100 elephant and some 411
buffalo, besides rhino, lions and lesser game." -from his book
African Rifles and Cartridges.
The OP's original question was whether the .375 was enough for Cape Buffalo. The Elephant thing was a mid-thread throw-in, out of curiousity, no? That hinted at his relative inexperience with Elephants, a condition I share. It can be surmised from the OP's question that he is not going to hunt an Elephant any time soon, and that if he does, he'll necessarily be backed up by a PH. and in that hunt a heavy load in a .375 for the OP might be "enough gun," if he can shoot it. The OP hasn't even started shooting medium/big bores yet, I'm assuming. There are 380 grain solids sold that he can use in a pinch....
The OP implies that he'll likely shoot plains game as well. If he hasn't got a suitable rifle for that, and he puts enough practice in with the .375 to make it an honest tool in his hands, then he'll be good enough (with an appropriate scope) to shoot plains game with lighter cartridges.
He asked about a scope. And since I've refilled my glass of Renault, here goes: He shouldn't purchase a .375 H&H without decent express sights. He should replace the rear sight with a ghost ring, a big peep. He might do well with a 1-6 or 1-8 quality scope for everything, mounted on good quick release rings, so he can test his peep on a charging wounded buff .....just as the PH's double roars. He'll see more than "hair" if he always starts the scope at 1x. This is getting expensive lubricating the writing, so I'll stop here, except to add the Taylor believed in the KO Formula (Bullet Weight x Terminal Velocity X Calibre /7000), which leaves out Sectional Density, modern bullet construction, and the given rifle's inherent accuracy. Taylor admitted much poaching and was, for that, driven out of Africa. Back in London he had two challenges. He was gay, but so were many leading (but discreet) cultural, military, and political figures of the day. But worse, his reputation for poaching made it impossible to get a job with H&H, Purdey, Churchill, etc. (Not that all poachers were evil. William Shakespeare was himself driven out of Stratford-on-Avon under indictment by a neighboring Lord for...poaching rabbits. So his indictment lead to my theater and reading pleasure.)