@KJE81 - I own several fine sporting rifles, from .500 NE to 6.5x54 MS. *And,* as the product manager of a premium rifle line within a large firearms company, I work with and have on loan every rifle and caliber you can imagine from .223 Win to .470 Nitro.
Yet, my go-to hunting gun has been and remains my .375 H&H Flanged. With it, I can take any animal that walks the Earth, from Africa's tiny ten to buffalo and even more. If versatility and a stellar track record on the world's game are what matters to you, you can't do better than a .375 H&H--and yes, in a double rifle or single shot the flanged version is absolutely fool-proof, in spite of how good the extractor/ejection systems for rimless shells have become in the last 20 years.
Besides the fact that it is not exactly a cartridge that you can find in factory-loaded form at your corner gun-store, it is available, it is absolutely a snap to reload and there are, oh, a million different kinds of bullets for it from practically every manufacturer. And bullets and brass are cheap and ALWAYS widely available, even during the bizarro-world time we're in (good luck finding a box of .450-400 without getting gouged!).
But the clincher is the perfect balance between hard-hitting, relative light weight, manageable recoil, and flat trajectory. With the 270-grain bullet--my favorite--you have pretty much the trajectory of a hot-rodded .308 Winchester with a 180 grain bullet, and you're surpassing the 4,000 foot-pound barrier with a rather generous margin. Load data--if you handload--is the same exact as for the belted version.
I frankly don't see any drawbacks to the other calibers that were recommended to you--IF YOU COULD HAVE AN UNLIMITED AMOUNT OF RIFLES. But if you're planning on investing big bucks on your ultimate one-gun worldwide hunter's toolkit, the .375 H&H has been the king since 1912 and I can't think of a single reason not to choose it for your project.
