I'd have to agree with those who suggest the .44 mag. Very versatile, shoots .44 specials till your proficent and confident with it. Less recoil in the .44 special and still has all the versatillity and accuracy. Then the cost of going to the bigger caliber won't hurt so bad, either. And, if your going to hunt, start reloading, the .44s have all and possibly more options than most any other caliber? Of course, all of the caliber options you've named, will do the trick.
Sage advice:As far as practice goes try the 44 specials. But in my opinion get your self a 22 pistol and shoot it. This will develope your trigger pull to the point where you won't need to think about it. All the while increasing your confidence and experience.
Very well put, longwalker