Well, the more common chokes are IC (improved cylinder), MOD (modified), IM (improved Modified), Full, Extra Full.

A IC and Mod pretty much do it all except turkey hunting.
With waterfowl stuff you will be using steel shot....which will make your mod choke behave like a full (or perhaps a IM)

If you wanted to buy one more choke I'd make it an IC, then a turkey choke if that's a season you want to take up. My 870 came with IC, MOD, Full. I've shot clays, squirrels, rabbits, doves, quail, deer, and one duck. IC and MOD have taken most of 'em. Nearly all of them!!! (well...except for the deer. I have a second barrel for that)