Mt.Man
I've taken 6 N.Y. whitetails with a handgun. 3 (two 4 pointers and a doe) with a 357mag and 3 (one spike and 2 does) with a 44 mag. Both were Ruger Blackhawks with open sights. I would suggest at least a 6" barrel. I used factory 158gr jhp for the 357 and 240gr jhp with the 44. None of the bullets past thru the deer. Longest shot was about 60 yds and most ran 35 to 50 yds.
Ear protection is a good idea but I found it bothersom for me when in the field. With my eyes getting older I found that I need to use a scope on my hunting handguns.
I wish you good luck at handgun hunting.