Are you talking about carrying a handgun as your primary hunting arm, or as an adjunct to a rifle?
If a
primary firearm, I would probably go with a .44 magun from S&W or Taurus (Ruger makes fine firearms, but I just like the S&W style better). If I was really serious about hunting with a handgun, I would probably go with a T/C Contender or Encore, though, in a caliber appropriate to the game I was hunting (although I guess some people would not consider a 14" bbl, scoped Contender a "real" handgun).
If I was taking one in
addition to my primary long gun, it might depend on the long gun. If I was carrying a rimfire rifle for small game, I might carry the same .44 mganum to have something for hogs or whatever. On the other hand, if I was carrying a centerfire rifle for big game (deer/hog/bear/whatever) I might want to bring along a little j-frame .22 for chance shots at small game.
This is of course assuming overlapping seasons for the relevent critters.