As has been said, the 357 will get the job done but....
....especially just starting out handgun hunting, I would also opt for the 41 mag on up.
The least legal cal. handgun cartridge to deer hunt with in Ohio is .357.
Years ago, it's what I started out with. Thinking the .357 would be the easiest to learn to hunt with in all areas, especially recoil. Found out since handgun hunting deer is much like bow hunting deer, I needed all the help I could get and soon went to the 44. , After a few years went to the 41,45lc and back to the .357.
The last ten yrs.or so, I've settled back on the 41mag as being my fav. as reloading is as much fun hunting. I can tailor my loads to what I'm doing.