If I were starting out, I would pick a 6.5mm and a 9,3x62mm and happily hunt the world over.
Adding further rifles would only be to fulfil specific roles such as a .458 or .500 for elephants or buffalo in dense vegetation where visibility is short; a subsonic .22LR for rabbits and squirrels; and a varmint/fox rifle such as a .20 or .222.