"Plan from when things go bad, not for when things go right."
With that advice, I go big.
The 338WinMag is a GREAT deer rifle. It duplicates the 270 on deer, but has more anchoring potential for elk, moose, bear. And works very well in Africa, see below.
The 300PRC is my North American second choice. (I've got a very lightweight ChristensenArms.)
I would also use the 338WinMag in Africa, and have, if allowed to my own desires. It is a great all-around rifle for walking a forest where a person might also bump into a buffalo or lion. If under a strict authority that might require .375, then in that situation, a 375. I like the 375 Ruger because it can be used in standard length (=30-06) actions. The 375H&H is functionally equal, though typically in heavier/larger rifles. But, where buffalo would be on a regular menu, then I would go up to a 416, either a handloaded Rigby or a 416Ruger in a standard action, (giving up 200fps to the handloaded Rigby).