.22 will be easy on your budget while at the same time (especially for beginners) you practice your aim, grip, stance, etc.
Trust me, cost build up soooooo fast shooting anything 9mm and up.
I you want a lot of practice and go easy on your budget, you have 2 options:
a) Get any gun you prefer in any caliber and get .22 conversion kit (for stater more expensive option)
b) Get a low priced .22 plinker and have fun (I recommend GSG 1911 about $350)
My first gun was GSG 1911 and i had so much fun with it (I still do), however, in order to get my black badge, soon after I also got a CZ SP-01 Shadow 9mm Luger.
I shoot both guns very often, but I am seriously considering getting a conversion kit for my CZ as well. It is great for practice!
Before you do anything, go to your range and try different guns, calibers and calculate your budget.
Good luck
EDIT: Regarding your shotgun sports I am not sure if .22 in any option can help you much. (I am, unfortunately wrong guy to talk about that as my knowledge there is slim)