I spent a lot of years in Texas where rifle hunting was legal. Typically I got 3 turkeys every year using a variety of loads. 30-06 with 110 fmj running about 1,900 fps. 22-250 55 grain at 2,000 fps. Never had to shoot over 25 steps. My bud used a Winny lever gun in 22 Win mag. Hunting there was a piece of cake due to flocks of as many as 200 birds during the fall season! Only long legged Rio Grandes there.
Moved to Colorado where in most areas a shotgun was required. Most shots have been over 35 yards. I mainly have used Federal 3" #6 and #5 copper plated. Works OK, but my patterns really start opening too much beyond 35 yards.
I use a shorter 20" barrel with a full choke insert on my old 870. I also have an old Bushnell Holosight mounted on it. Center their head in the circle and slam the trigger. Seems to do the job on our handsome Merriams in the mountains and Rio Grandes on the plains.
Oh and a decoy can make a world of difference in how close they come! Made my first from papermache before they were ever in production.