Depends on what you want. Single shot, revolver, semi? How far you plan to shoot?
In a revolver, I would go with a 44 mag, which you could shoot 44 special out of, or load the .44 mag down a little if you are concerned about recoil. I used to use 200 gr bullets which recoiled a little less and still did a fantastic job on whitetails. Or a .45 Long Colt. Very manageable recoil and does a great job. Not a big fan of a .357 for deer.
In a single shot like a T/C, the choices are many, 308,7-08, 35 rem, among many.
I used to hunt exclusively with handguns years ago.