I would have taken my custom Brno .375 Ultra, but left it at home because I didn't find out about the requirement for an In-Transit firearms permit until there was too little time to get the paper work through. This was a huge disappointment to me, but I didn't want to risk loosing a $4500 rifle. My travel agent booked me through the US, and surprising to me at the time, the US is anal about non-resident guns being flown across the country.
If you are not hunting anything dangerous, any general purpose North American big game rifle would be fine for Africa, and one rifle is enough considering the baggage weight restrictions. Typically ranges are not excessive, so any cartridge from 6.5 to .30/06 or .300 Winchester will do just fine. I would load a premium bullet and use a single load for all my hunting. A variable low power scope will be useful as some shooting will undoubtedly be very at short range in heavy cover.
Should you decide you want to take on dangerous game, a single rifle in the 9.3, .375, or .416 bore size will work fine for both your dangerous and plains game. You don't need a stopping rifle, that's the PH's job . . . just hope he's good. You may want two loads, one solid one soft point, although chances are you would do just fine with the heaviest TSX's you can load for your cartridge. I shot all of my plains game with a M-70 .375 and flat nosed solids, and found it killed as well as if it had been loaded with soft points.