Well, no. The most available may well be the 7X57mm. It has a long lead over other 7mm's, since 1892. And Euro ammo makers load it hotter than is normally the case in the USA. Study the Brennecke Torpedo Ideal and similar bullets. DWM and RWS ammo. Norma of Sweden also has some good bullets.
Look: you need some background here. Find, buy, and read Jack O'Connor's, "The Rifle Book" and, "The Hunting Rifle." They're a little dated, but have the background that you need. Nothing better has come along since Jack died in 1978.
You also need the latest edition of, "Cartridges of the World."
Until you do this basic homework, you are just a babe in the woods. Pay attention to what O'Connor wrote about throating in the 7X57mm, which was among his (and his wife's ) favorite cartridges. Eleanor shot a lot of animals with the 7mm. Her "heavy rifle" was a .30-06, with which she shot a tiger! (Back in 1955, that was legal in India.) But most 7X57mm's are throated for the original 175 grain bullet, which can still be a good choice. One of the main reasons why O'Connor switched from the 7mm to the .270 is that his 7mm barrels eroded too soon if mostly lighter bullets were used. He preferred 139 grain bullets in the little 7mm. But Eleanor used mostly a single 160 grain bullet on all species of game. He hand loaded her ammo, to some 2650 FPS from a 22-inch barrel.
But anyone hunting in a particular area needs to rely on his outfitter to tell what ammo and laws exist there. They will also need to be involved in the process of getting licenses and hunting blocks/zones.
You will also need to determine which species cannot be legally imported into the USA. It may be legal to kill, say, a jaguar, in some countries, but not legal to bring the hide back here. The new laws pertaining to ivory are especially distressing.