With that gun and choke you can likely kill a bird with any 3inch #4, #5 or #6 shot out to 30 yards and with modern turkey loads take one easily at 40. The patterning and preferred shotshell combo really matter for shots under 20 (when most turkey loads resemble a golf ball) and those over 40.

I give that intro because you can choose a single box of modern turkey ammo off any shelf, take a few shots to get a 'feel for it' - and then most likely kill a turkey with a well-placed shot under 40 yards. I'm sure some of my fellow board members will cringe when they read those thoughts, but IMO it's just the reality of modern weapons and ammo is that they really are that good. Knowing the pattern is still critical for success, especially when you misjudge distance by 10 yards, but not as critical as it was 20 years ago...

You'll get various answers to your questions, largely because most of us have found a 'special ammo' or something that just consistently shoots well out of multiple guns.

Personally, I prefer any of the Winchester ammo. I've shot them with good patterns and success from a Mossberg, a Winchester, a Weatherby, and an Ithaca. I'm currently using Winchester Longbeard XR in my 12ga Ithaca, last year's bird was dropped cold at almost 55 steps. Hevi-shot triple beard blend performs great in my son's 20 Weatherby with a Hevi-shot choke, but it doesn't have enough killing power past 40 yards - and all my other guns shoot it like crud.

If I was new to turkey hunting and had no baseline, I would probably start with the cheapest Winchester #6 shot you can find - probably either Double X or Supreme. If it's got a scope that you need to zero, you can even start with #8 target load to get it relatively centered. It's typically about $1 per shell or maybe less. If it patterns well, and you're worried about shooting birds at longer distance, then the Longbeard XR will likely pattern almost the same as the Double X and extend your range by 15-20 yards.

Note that pellet size is largely personal preference - obviously you will typically have a denser pattern with #6 than #4, but the kinetic energy is greater per pellet with the larger shot. With that said, any of the newer loads - the 3inch Longbeard XR or the Hevi-shot lines - will consistently kill birds at all shot sizes out to 50-60 yards if the gun patterns well (hence, my comment about pattern mattering for longer shots)...