Congratulations on your new gun. I know you'll love it.
I've been shooting a Winchester Super X3 (same gun internally and the same barrel) since September of last year. I used it for fall and turkey hunts and am very pleased with its performance and handling.
I tested a number of different turkey chokes with this gun and settled on the Strut-Stopper Xtreme (SSX). I shot it with all the different brands of "hard" (tungsten-based) shotshells as well as several lead loads and it did well with all of them.
I recommend that you try that choke and also that you consider #6 shot. The #6 shot just "flows" better than the others and with multiple hits, you'll have plenty of retained energy to cleanly kill a turkey at 40 yards or even beyond.
If I can be of help in any way, don't hesitate to contact me and I'll do all I can to be of assistance.
"If he's out of range, it just means that he has another day and so do you."