cylinder should be good enough. only takes one to stop a rabbit. full choke decimates em with bb loads. the times i use a 12 gage on rabbit i use #7 shot that you typically use on skeet. rabbits are super thin skinned.
since you are using large shot you can get away with a open choke. I would use an improved cylinder choke for BB shot. Most of the time BB shot are high brass loads, which means you have more pellets per shell.