Here is my thoughts:
If you plan to use it primarily as a hunter, go with the .44 Magnum caliber. A 4-6 in. barrel should be sufficient. Any longer and it starts to become very nose heavy. The Ruger, Taurus or Smith and Wesson types should all be fine.
If you plan to use this very often as a carry gun, get the .357 Magnum in Smith & Wesson, either a model 19 or 66. The 686 would also be good. A 2.5 in. barrel would be perfect for carry. But a 4 in. isn't bad at all and would be a good choice if you choose to carry it holstered on the hip. And the .357 will be plenty sufficient for deer, I took my first deer with one (nice 5 point). I would go with the 4 in barrel for this purpose though.
Now if you plan to hunt and pack equally, get both calibers. A big 44 and a nice carry size .357. **** However, you may want to avoid my advice as it always leads to reasons why you need a new gun, I do myself that way all the time! LOL