Ive shot all the hand guns you have mentioned.
The .44 is by far the best all purpose choice for hand gun shooting/hunting.
The .460 is ok, if you use the 454 Casull loads, and arent shooting too much.
The .480, Im not sure really what I think about it. Id have to shoot it again.
The .500 is way too much over kill and is a gun you shoot once and put down. (Will never shoot again)

In my opinion the best choice would be a .44 or a .454 You really dont need anythign bigger than that in the US.

Get a well made .454 and you'll have it covered. The new .460s and .500s are cool but too much of a good thing imo(too big and heavy). With a .454,you can shoot .45lc for practice. I realize you can shoot both in the .460 but why bother? If you can't do it with the .454 you need to practice stalking/hunting.

44 mag will be in a lighter package, and cheaper to shoot. The 460 does have extreme capabilities, the ability to shoot 454's and 45 LC which does make for lighter recoil and less expensive plinking.