A 20ga will work fine, just equip it with a full or extra full turkey choke. I shoot a Rem pump 12 ga with a 21 in barrel, I got the same gun in a 20ga and it works just as well, with less kick. A good buttpad is always a good investment and they don't cost much, and reduce any felt recoil to little to nothing.

I'm not sure just what he is saying about using a sawed off gun. But as far as a choke vs no choke. No choke at all is going to widen your pattern and lessen your chances at getting the pellets where you want them. Think of it this way, on a garden hose spray nozzle. If you tighten the nozzle, you are going to constrict the flow to a fine stream. Much the same as using different chokes on your shotgun. A full or xtra full choke is going to constrict your pattern down, so that your pellets are going to a minimal spot, at a greater distance. Hence, more pellets in your turkey. Then, you need to find the best brand and shot size that works best in the gun you're using.