factory
I've shot a Rem 870 at gobblers for years, mostly with a 20" rifle sighted slug barrel, and a factory Rem Super Full turkey choke, the one with the knurling on the muzzle end. Rem makes a turkey choke with a slightly lesser constriction and I think they call that one Turkey Extra Full. They also used to make one called the "Ventilator", which had multiple ports and was their tightest set up, but it is my belief that it is discontinued, and I have not ever used one. I shot the Extra Full for a few seasons, then switched to the "Extra Full" and never regretted it.
Chokes and ammo are interdependent, and you can spend a ton of money experimenting and finding a combo with which you are satisfied. I know a few guys who have spent enough for a new gun, if not two, in search of of the ideal combo. The Remington factory turkey chokes are affordable and should offer good results when paired with premium ammo, to clobber any gobbler you center at a reasonable range.
My preferred load is the Winchester "XR" lead, 3 inch, #5 shot, 1- 3/4 oz ( I think that is the correct payload weight). In my set up, it is the best performing lead load I have ever shot. It will shoot patterns that equal or exceed older, heavier shot charge loads of smaller shot, while still delivering heavier pellets at higher velocity. The XR lead load is the one with the pellets encased in an epoxy mix.
Finally, as I always do, I suggest you look into some type of sighting system for your gobbler gun beyond the traditional single bead. These new loads and good chokes deliver patterns that are tight enough to miss with at closer ranges and require good pointing to center a gobbler at even moderate ranges. What ever your choice, a dot, or fiber optic front and rear, or a scope, go the extra distance and fit your gun with good sights.