I have personally kill over 10 mule deer. The longest shot was 50 to 60 yards. Only 2 were body hits in the heart/lung area, the rest were head shots. These kills came with the lowly .38 Special and Rem's 158 LSWCHP.
The head shot deer were DOA on their way to the ground, the heart/lung shot took the usual 2 minutes, 53 seconds to totally expire.
In all honesty, I always thought that a heavier caliber would be more approperiate. But because of the reduced recoil, I could shoot that 4" revolver .38 Special and place the bullet exactly where I wanted it. It's hard to argue with success, Still, I wouldn't recommend the .38 as a deer round.
Shooting deer with a handgun is much less desireable than shooting with a rifle. Keeping that in mind, if a handgun round doesn't kill with the 'thunder of thor', don't be surprised if a failure comes when using a handgun.
As a side, an aquaintence of mine who passed away, used to take elk with the .357 mag. with a model S&W 19, 6" bbl., 158gr bullet. All were heart/lung shots under 50 yards. He never lost one. He always said that the elk either drop in the tracks or didn't go far. His comments to me were, "I wouldn't hesitate to shoot an elk with the .357 mag." This isn't a recommendation, just fact. I don't know how many elk he took, he was a terrific shot, and he was a distant friend with the immortals "Skeeter Skelton/Bill Jordan."
In regards to barrel length, I've carried a handgun almost all my adult life. Either professional or personally. I've found that anything longer than a 4" barrel is a pain-in-the-ribs proposition. Meaning when you sit down with a 4" barrel, it doesn't jab itself into the ground/seat and the grip is pushed up into your ribs. IMHO, I have no problem giving up a few feet of velocity for the extra comfort. Plus, I'm somewhat lazy and like to sit. No charge for the extra info.
Dewy, I hope my experience helps in your decision making and I hope you Fair Well in your hunt.
My .23 cents (inflation)