I'd second that and also say, pick up a Ruger Mark-II...This is a .22 pistol so you can learn to shoot fairly cheaply...

I've got the Mark-II, Ruger Blackhawks in both .357 and .44 mag as well as a .40 Glock...The .44 is a hand full to shoot, with the .44 Specials it's not bad but with full house loads the .357 is a ***** cat to shoot...

I've had to put down quite a few whitetails while taking guests on our farms...What I've found is if that deer is down and immoble, you can walk up and put a .22 in it's brain...So any of these calibers will work...If that deer is able to still go, you're not getting close enough to dispatch it...It's also very hard to get close enough in the dark, hold a light, see the open sights and finish it off...

All that being said, my deer hunting handgun is the .44...My deer dispatching handgun is whichever I have close at the time, they've all done the job in the past...The .357 would be a good choice and could be used for hunting with the heavier loadings...