My favorite handgun for deer is a S&W 629 44 Magnum. I like to use a 240 grain Keith style bullet (Semi-Wadcutter) moving along at about 1500fps.

While practice is important when considering hunting with any type of firearm, it is much much more important with a handgun. Handguns are much harder shoot well than a rifle is. If you are the kinda guy who shoots very little, handgun hunting isnt for you.