I shoot a double gun on sporting clays or skeet, I usually leave mine alone and leave it at cylinder and improved cylinder. My wife changes hers all the time between skeet, IC and modified.

For a single barrel, I would probalby put in a cylinder.

We might do some skeet esp. for people new to it and for that you want as wide open as you can get. cylinder or a skeet choke. But of course, most good people (not me) shoot skeet with a .410 so......

If I had to pick one I'd say IC.

oh distance:
skeet from 10 feet to the longest shot is about 20 yards.

sporting clays can be from 10 yards to really as far as 60 yards (but to be honest, nobody hits those anyway, so why bother?) most shots are from 10 to 30 yards.