Re: 12 gauge; 2 3/4 inch
Being lucky enough to grow up in the area of Oregon where all of the turkeys were planted I got to hunt them a ton.
I found that a 3 1/2" is just too much for nothing. A 3" mag is fine, but if you're a good shot a 2 3/4" high brass will give you the best distance performance. The bad part is they don't make those anymore in 4/5/6 shot. In a similar brand/load you'll get the same powder charge for all three lengths but as you get longer the shot weight grows and slows down the round making it less lethal at distance.
So, now that all of my old Federal Premium 2 3/4" reserve is gone I've found the Winchester Double-X High Velocity 3" are a great substitute and pattern about the same out to 75 yards.
The biggest thing is find the choke tube your gun likes. There is absolutely no substitute for it. It might be a $20 one or it might be one over $100, but you need to find it. I can't recommend a specific one. My 835 is 19 years old and a Strutt Stopper is the best I've found for it so far. A buddy has a three year old 835 and the stock extra tight from my 19 year old 835 works best for his.