If you are serious about hunting dangerous game in Africa, a quick check with a licensed PH will tell you that by law in the countries they are licensed to accompany hunters that usually a 375 H&H Magnum is the minimum caliber allowed for dangerous game.
Dangerous game begins with the cats and goes up to the really big stuff like elephant, cape buffalo, rhino, hippo, and so on. Basically anything that will bite back on their terms if given the chance.
Most PH's prefer a bolt action controlled round feed magazine rifle with safari style sights dead on at 50 yards or a very good and extremely durable low powered scope with solid mounts with easy to acquire cross hairs. Many also like the various double rifles, but they get to be extremely expensive to have built. What ever gun you choose the PH will want to know how well you can use the rifle as this will dictate how he does his job to some degree. His job is to protect the hunter at all costs and still not kill game not being pursued just because you happen to cross paths with it. That puts the PH and his reputation and even his job between you and the game when you first encounter an animal. If you have a license for the game the PH will direct you from there and he becomes the back-up, albeit a VERY RELIABLE BACK-UP.
Some useful cartridges are the 375 H&H, the 416 Rem Mag, 416 Taylor, 458 Lott, and 458 Win Mag which all can be had in normal sized and available bolt action rifles at a reasonable cost. If you have the money for a good double rifle, some of the old English metric cordite era cartridges from the early 20th century might get used. For large NA bears, the 375 H&H is great as are any of the bigger cartridges. Quite a few big bears have also fallen to a 338 Win Mag with heavier bullets and to lever action 45-70 bullets designed for penetration. Personally I prefer the 375 over the 338 because of normal ranges the big bears are encountered at. A lever action 45-70 works for bear but would not be my first choice.