I'll vote for the .458. The round is surprisingly versatile. Loaded with a 500 gr solid the .458 will work on elephants - in a pinch. The 450 gr X bullet can be driven to 2200+ with some tricky reloading techniques, a combination suitable for most large/dangerous game benefiting from the use of an expanding bullet. Cast bullets can be driven slowly for small game hunting, or fast enough to harvest any North American game. The 480 gr bullet from MT Chambers is a good choice. Rifles can be found in the affordable range - something not always true of the over .40 club, and components are available and affordable. A Ruger #1 is a pleasure to own and shoot, but if a bolt gun is more your cup of tea, there is lots to choose from.
If you want a true magnum length cartridge the .416 Rigby is a fine choice, but it is viewed as a medium bore by many - although a very capable one. I would go the custom route and get a .460 G&A built - think .458 UltraMag. This cartridge will drive a 500 gr Hornady to 2400 fps, the velocity that many African professional hunters consider Nirvana. Aside from the great ballistics, the G&A can easily be made from .375 Ultra brass, which is both affordable and available.