9.3x57 is perfect for about any North American Game. You can used sized down 225gr. Hornady's at 2,550+ fps for deer and black bear, on up to 270 to 286gr. Speer, Privi's, Hornady's, Normas, etc for heavier game. My 94 action easily does 2,200fps with 286gr., 2,300fps with 270's, 2,450fps with 232's and 2,550fps with 225's. Large game is easy picking to 300yards and if you want to extend the range on deer and antelope, 400 is possible with the lighter bullets with a bit of practise.
Too, the 9.3x57 has very moderate recoil and is easily shot by any man and most women.
A .375 on the same case (or improved 57mm. case) would also be a great choice. Hornady makes dies for it.