Shot size and speed debate, my 2 cents. Lots of super advice on this thread.
Kinetic energy = 1/2 mass * velocity* velocity. Since we shoot turkeys in the head and neck (right??!!!!), our needs for inertia are pretty minimal, we only need enough penetration for our pellets to penetrate skin and skull, and/or a minimal amount muscle and skin to reach the neck vertebra. Beyond that minimal need for inertia (which is positively related to increasing projectile size), we want to maximize velocity and not mass of the pellets, since there is a linear relationship between energy and mass, while energy increases with the SQUARE of the velocity. In English, we only need enough pellet size to penetrate to the central nervous system, after that we want the fastest pellet possible.
Within these constraints, we want as many pellets as possible hitting that head and neck, so patterning your shotgun is critical. Under 50 yards, any load with #6 or larger, lead or heavier shot; that consistently puts 6 or more pellets on the brain and vertebra of a turkey head and neck silhouette target (hint: buy one and copy it! you can find downloads online too), has adequate killing power. I recommend holding shots under 50 yards, pattern density of the larger pellets is too low, and velocity declines too much with the smaller pellets for adequate inertia or energy. Yes, unethical hunters get lucky out to 80 yards and beyond, but ethical hunters only take high percentage shots.
My favored load is a 2 3/4", 1 5/8oz, max. dram equivalent Remington duplex 4x6. I don't know if they make this one anymore, after I did extensive pattern testing in 1990, with the same full-choked Winchester 12-gauge pump, I bought a large supply. Over the past 18 seasons, I have fired around 20 shells. I have missed once (Mexican stand-off over a hogback ridgetop in Nebraska late 1990s, shot at his head when he flushed, under 10 yards), and had one bird that required two shots (38 paces, he jumped up and flew, lots of little neck feathers at the shot site, I found him badly hurt about 400 yards away after an anxious 2 hour search. I shot his face off at about 10 feet, he had numerous pellet holes in his neck (13 I think), none of which damaged the spine - the pattern gods frowned).
I hold myself to 40 yards, even though pattern density was adequate to 55 yards (6+ pellets on target), most of those were #6 pellets that I worry about KE at that range. At 60 yards, that drops to 0-1 on target.
My bottom line: the fastest, smallest pellets, down to size 6, that pattern well, and shots held to under 40 yards. That has not been a hardship, most birds I've killed were under 25 yards before everything came together.
One last observation: I killed a bird in Wyoming with OVER 40 #5 lead pellets in his body, yellow/purple and HEALING. Amazing that bird was still alive, much less gobbling and breeding. I'm sure whoever shot him first, still wonders how he got up and flew away. DON'T BODY SHOOT!
Good luck to everyone!