RE: 2 3/4" vs. 3" ?
From a technical point of view the reason for the 3" shell is all about space and/or room to fit the extra components into a hull. It doesn' t always happen because every gun is an entity unto itself, but usually a 3" shell will put more shot in a pattern than a 2 3/4" shell because normally they contain more shot to begin with. While it is true that the 3" shell due to the heavier payload will sometime shoot at a slower velocity than a 2 3/4" that isn' t always the case, and the difference in velocity in not enough to worry about.
If your going to hunt turkeys and geese I would certainly encourage you to buy the 3" chambered gun. It just gives you so many more options for specialized loads. 2 3/4 will work and work well. In fact that is what I shoot most of the time. But the extra shot in my pattern at the 40 yard mark is a plus especially in the turkey hunting world when the margin of error can be very small.
As far as a 3 1/2" 12 gauge. They hold no interest for me. If I want to use a 3 1/2 inch shell I will use my 10 gauge. I HAD a 3 1/2 inch twelve gauge but did not feel the performance I was getting with the 3 1/2" shell vs the 3" shell was worth the pounding I was taking. I still have to find a home for two or three boxes of 3 1/2" T-shot from that beast.
I realize not everyone will feel the same way I do but that is okay too.