You're going to get a lot of advice to buy something in 3 1/2", but I'll jump right out there and disagree. You don't need anyting more than a 3" gun for anything you can hunt with a shotgun, and in all honesty, a 2 3/4" gun is fine for over 90% of what you might shoot. I do use a 3" full choked gun for turkey hunting, but I'd venture that over 80% of the birds I've killed could have been shot just as well with a tight choked 2 3/4" gun, and frankly a 20 guage would have killed a bunch of them stone dead. For geese, a 3" gun has some advantages, especially if you shoot steel, but if you're shooting decoying birds a 2 3/4" gun would again work fine for most situations.
I may be an old dinosaur, but I've been using the same 2 3/4" gun with a 26" improved cylinder barrel (with NO choke tubes) for the last 28 or so years. Over that time, you don't want to know how many ducks, geese, pheasants, quail, doves have fallen to that gun. The only thing I don't use it for is turkeys, but that's becuase of the open choke, no other reason it wouldn't be a great turkey gun. By the way, I have plenty of other shotguns in my cabinet, including plenty of 3" guns. I won't have a 3 1/2", as they don't handle as well and can't do anything that a shorter chamber gun can do too.