After an incident where my Remington 7400 jammed after critically wounding a large buck (that I did not want walking off), I pulled a Colt 45 Auto off my hip and finished the 12-point at 70 yards (the 185 grain Golden Saber +P performed amazingly)...

The Colt 45 is a personal defense gun (primarily) and a backup (secondarily)...

That said...

Avoid the .357 for work on deer (it would easily finish a deer, but would not be appropriate IMO for a primary gun)... the 10mm, 41 Magnum, 44 Magnum, and 45 Long Colt are the calibers you should consider...454 if you are really dedicated and looking more for a primary... Although I carry a .45ACP during rifle season, I would not recommend it as a primary...

My favorite hunting handgun is the Ruger Blackhawk convertible in 45 LC / 45 ACP with a 5.5 inch barrel. 45 LC standard/SSA loads are great for practice, use Corbon or Buffalo Bore loads for hunting ***these are heavy loads***

As mentioned consult your hunting regs to make sure whatever you are using is legal...

Sight in at 50 yards, but keep your shooting to a range where you can consistently put the rounds in a pie pan...