you said you had an H&R single barrel but did not say anything about length of barrel or choke.if it is a full choke,and you gun is chambered for 3" shells,i would try federal.win prem or rem hevishot turkey loads to see which has the best pattern at 40 yards.the full choke probably would shoot 5-6 shot better than #4 and a mod barrel might shoot the 4-5 shot better.most single barrels i have owned were full choke.you just have to start trying to find which load it likes best and what is the best range for that load.also,be sure and see if your gun is chambered for 23/4" or 3" shells.if you don't have a turkey target,get a piece of cardboard and a majic marker and draw a turkey head and shoot at about 40 yards.whatever range you can put several pellets in the head and neck to make a clean kill, will be your effective range.get this project done and determine if your gun will be ok to kill a turkey or not then you can go to the next step.