I have an modified fixed choke with the gun I am using now. I also like improved.
I would stay away from full unless you plan on taking long shot. I have a buddy that only had a turkey coke for his gun and used it when we when pheasant hunting in Illinios. Ruined half the bird.
Depends on a number of things...shot size, specific birds to be hunted, shotgun guage.
For pheasant the ideal is a double choked modified and full. A single barrel is best modified. #4#5#6 shot are all good...I prefer#5
For grouse I like improved cylinder or a double choked improved/modified. #6#7.5 shot
Waterfowl has a world of posibilites.
Goose: I use hevi-shot BB over decoys with a modified choke. This kind of limits your range for passing shots. For passing shots a full choke is good. Again a double with modified/full is good
Ducks: over decoys #2#4 hevi shot with a full choke.
For jump shooting I use improved cylinder with 3.5" #4 shot. The idea being an open choke with a lot of pellets will have a big pattern with the best possible pattern density.