Plains and prairie birds: 12, 16 or 20 with 28-inch barrels, your choice of action. Currently, mine is a Ruger Gold Label, a light 6 ½ pound 12 double. It has an aggressively forward balance that makes it swing like a heavier gun, which is what you want on the wide-open spaces.
Birds in the brush:** 16, 20, 28 gauge with 24 to 28 inch barrels and very light weight. My grouse gun is an Ithaca/SKB 100 20 gauge. These Japanese doubles were ahead of their time back in the 70s. Mine has 25-inch barrels choked IC/M (SK/IC would be better) and weighs 5 pounds, 10 ounces.
Turkeys:** 3-inch 12 or 20 gauge pump or semiauto with a 20-24-inch barrel and some type of sights. I like pumps for turkeys because it means I can make the excited launch from a sitting position to a flopping turkey without worrying about a live round in the chamber. Right now I am enamored of a 20 gauge 870 with an Undertaker choke tube and a Zeiss Z-Point sight.