Quite honestly, it will be fairly hard (not impossible) to find a gun to cover both home defense and hunting situations. I would first ask where you are from, and where you will be hunting, and what the laws require for hunting pistols. Some states, especially out west, only allow the use of cartridges as long or longer than the 44 Rem. Magnum for hunting big game. I am not sure about the states back east at all. Just looking at the regs will narrow your search down very quickly.

The reason I say it will be hard to find a weapon to use for home defense and hunting, is that home defense weapons are not designed for hunting, and vice-versa. Most full power hunting hand-guns would be so powerful, that you would not get the desired effect in a home defense situation. Not very many factory loads are available for home defense in typical hunting calibers, and vice-versa.

With that aside, two cartridges that are good for deer hunting, and quite popular are the 44 Rem. Mag. and the .454 Casull. Both rounds will accept their smaller cousins of the 44 Special, and the 45 Long Colt. The latter two MAY be good for home defense IF you can find a good load with bullets designed for home defense. The first two are exceptional cartridges in their own right when used in the right application, and within their limitations in the field.

Another draw back, is that hunting handguns have to be fairly heavy, as compared to home defense weapons. You want full power loads for deer, but don't want to break your hand every time you pull the trigger, and also don't want something that can be just plain cumbersome to try and dig out of the night stand drawer.

My advise would be to get a short barrel for your 20 or 12 guage (presuming you have one) for home defense, and then buy a specialty handgun for hunting. Load the shotgun some larger shot, like #4's or 2's, and it will not penetrate into the next neighborhood like a full power load from a 44 or 454.