I used to use a double barrel 12 gauge with a modified and full choke...Out to 35 yards, it would put 6-7 pellets into the head and neck out to 35 yards, using Remington high brass 2 3/4 #6 shot...I killed several birds with it, did just fine...

When I bought a B-80 back in the 80s, I purchased a Hastings .665 choke and tested several shells and shot sizes...
For some reason, it puts more #5 shot into the kill zone than it does #6s, go figure...Now I'm putting 12-15 shot into the kill zone at 40 yards, using the 3 inch Remington Nitro ($5.88 at Walmart) #5 shot...The furtherist I have ever killed a bird with this setup is 30 yards...

The point being, try several loads and see what the gun patterns the best....My gun shoots Winchester Supreme turkey loads high and to the right...The Federal Premium 2 oz loads put less pellets into the target than the 1 5/8 loading of Remingtons...If your gun prefers #4 shot or #6 shot, that's what you should use...