Have you done much shooting before?
If not, the .22 is the learning platform. Minimal noise, minimal recoil, minimal cost. All shooting principles can be learned on a .22. You can go out by yourself to practice with it, as opposed to a 12 gauge which you will need someone to throw the birds or activate the thrower. It is legal in most localities (even here in New York State) to purchase a rifle or shotgun used from an individual. There would be your best deal. Stick with known names in a bolt, or single shot for learning safety. Marlin makes very good and inexpensive guns, there are a zillion out there, and you should be able to get one used for around 100.00.
A shotgun combination (buck and bird barrel) makes great sense if you are in with a shotgunning crowd, with access to a skeet/trap field, or even a place to throw your own birds. just blasting at cans, paper etc. gets old real quick though, and darn little in marksmanship will ever be developed without a purpose. For target shooting, 12 gauge slugs will prove very pricey and painful.