Agree on 12 gauge and 22 LR.
Substitute 30-06 for the 300 magnum. (the old 06 will do 99% of what a 300 will do you just lose about 100 yards at the far end of the spectrum where very little game is shot anyway.) 30-06 has factory loads from 55 grains to 220 grains...pretty versatile and just about anyone can handle the recoil. You can find ammo in any store from Anchorage to Cape Town.
If larger game is planned, then I add the 375 H&H Magnum. It will throw a 270 grain bullet as flat as a 30-06 with a 180 grainer but it punches way above its weight. You can find ammo anywhere on Earth big game is hunted from Anchorage to Cape Town. The 300 grain load will handle really big animals better. It has been laying out game from Dyker to Elephant since 1911. It works fine on whitetail deer...I know. It is about as close to the perfect all around cartridge as there is.
Also on the BIG game side I vote 458 Lott. It will easily push a 500 grain bullet to 2150 fps. That has been the standard of all the old British nitro express rounds and they were proven Stoppers on all the really big animals like elephant, buffalo, hippo. 458 Lott is becoming a standard of sorts. A friend of mine went on a hunt to Zimbabwe about 8 years ago. His rifle made it to Zim with him, but that airline sent his luggage including his ammo to Mexico. It was not hard for the PH to come up with some Lott ammo in camp when he got there.