Given the efficacy of modern loads, most any shotgun properly choked will pattern well enough to kill gobblers at ethical ranges. .410, 20ga, 12ga, pick your poison. Whatever you choose, pattern that gun and know what it's capable of. Plenty of good info in the turkey guns section of the forum. Lots of incredibly knowledgeable people.
As for POA, most consensus is the base of the neck. And you want to wait till the moment the gobbler lifts his head (not when he's strutting, not when he's gobbling, not when he's pecking around). A soft cluck on a mouth call is usually plenty to get him to stop and get his head up.
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