RE: 22 17 22 250 which one
Technically the gauge shouldn't matter on a shotgun. Power output is the same irregardless. You just get less shot is all. Doesn't matter whether you use a 410 or a 12 ga ballistically. A number 4 pellet moving at 1200 fps is a number 4 pellet at 1200 fps. Doesn't matter which gun it comes out of. The rub is the larger gauge guns let you shoot more shot at the same speed. Which gives you a more dense pattern and often extended range. And you can probably get more speed out of a 12 ga as well if you go with lighter load.
So I'm not saying a 28 ga or 410 will not kill a turkey, because they will obviously. Just that it puts you at a disadvantage over a larger ga gun that can throw a more dense pattern at longer ranges. And the 20 and 12 have more options on shell choice as well.
Honestly for me, if I lived in an area where I could use a rifle for turkey I would use the 17.
Paul