I would not enjoy being forced to choose a single shotgun and pursuit, the only way I can see it being acceptable to is to first sample all the various great shotgun hunting in all the legendary places across this continent with every shotgun that strikes my fancy.
Waterfowl I'd have a hard time giving up my Browning Auto 5 Mag 12, but I'd have a even harder time accepting I can't use a 20 gauge or double or pump gun when the fancy strikes me. Waterfowl would probably be my pick, locations, foul weather, decoys, variety of tactics and it is just one of my passions. I have a hard time making time to hunt anything else when Autumn arrives.
Upland may take it though, I had a good pointer like a Brittany or Griffon I could happily hunt with a 20 gauge and I would probably reveal my unrefined and heathen nature and pick a 26" barreled 870 Wingmaster with a 3" chamber and choke tubes, since I consider turkey upland game. I know it should be a Ithaca or 16 gauge at the very least, if not a classic double.