Danny your 20 ga. will work fine. GO pattern that gun.......here is a link to the target I use.
I only count pellet holes in the skull, eye, neck bones8 to 12 is my rule of thumb for a really dead turkey and that pellet count dictates my yardage - though I try to call em in under 20 yards. Try 4s, 5s or 6s copper plated lead = penetrates better,

http://lewand.tripod.com/turkeytargets.html

now in some states it is legal to use a rifle.....not all tho...check you regs.....and turkey huntings' ultimate goal is you call em up close and personal!

But check that a 22 is legal - tho I advise against it. If it is - nd that is what you so chooseaim for the head.....

any body shot - especailly with a shotgun - all ya got is a wounded bird that can get away - quicker than you can imagine.

JW