I think the key to this question is the "remote" issue. You want rifles with a broad range of usefulness, rather than what you'd like to have, if you were on a three gun safari. And you want ammo to be readily available.
I would have:
1. An everyday rife, which for me is a .300 Win Mag - ammo is found everywhere (where ammo is found!). But anything from about a .270 to about a .338 would do for an everyday rifle;
2. A large rifle for the big stuff - in my case, a .404 Jeffery or a .416 Rigby. While neither of these is the best charge stopper, either will handle everything there is in Africa, and the ballistics are pretty good, allowing you to reach out a bit more than some of the bigger calibers without having to aim at the sky. But again, anything from about a .375 to .458 would do for a big rifle. Bigger than a .458 you're getting into specialized rifle territory, and doubles don't have the range, so I would limit my big rifle to a .458. You can make it a Lott if you really feel the need, but it's not necessary. For those who say that the bigger Weatherby's will also work, I agree, but I don't like Weatherby's, so they aren't invited (plus ammo is hard to find in Africa).
3. Lastly, a 12 gauge shotgun. In a remote area a shotgun would be far more useful than adding another rife, both in terms of shooting and self protection.