Getting good with the .22 first is good advice. The much shorter sight base can be difficult for some people.
After that it depends on what type of gun do you want to use. If you go with a revolver, I would stick with the 44mag. I have talked to a couple guys that have had less than ideal shots with a 357 and there is not as much room for error.
That being said, my only pistol killed deer came from a S&W model 29 44mag. It was a nice gun, I just realized pistol hunting wasn't for me.