Rooster,
some thoughts- First, I would pattern your Winchester with the full choke tube it came with, using whatever load you want to use for turkey. There are a lot of choices out there, as well as arguments as to the best shot size. Personally, I shoot #5's with great success over the years. My average shots are between 20 and 30 yards.
Patterns should be sufficiently dense at normal ranges to put a lot of hits in the head and neck area of your turkey target, with out a lot of gaps in the pattern. It also tells you whether or not your shotgun is shooting where you are looking.
I am also a firm believer in fiber optic sights, front and rear. With tight chokes and only a front bead, it is entirely possible to miss- seen it too many times. If your shotguns have vent ribs, these sights are a simple add-on.
Just remember- folks have been killing wild turkeys with shotguns for many, many years, long before all the fancy stuff we have available to us nowadays was even thought of. Tighter chokes, better ammo, and better sights simply up the odds of making a clean kill shot.
As far as chokes go- there are a ton of aftermarket chokes available. If you can swing it, try more than one in your shotguns, as well as a brand or two of different ammo, to see what patterns best. No one choke, or ammo type, can be prescribed for your guns, they are all different in performance.
