I also have a Beretta A300 Outlander and have Modified, Imporved cylinder and a Teague skeet choke. I mainly keep the Modified in the gun as it is the best all rounder i have found from rabbits and foxes to pigeons and rooks, recently however i have started to use the improved cylinder for closer targets such as decoying birds, to good effect too, but i prefer the modified as you just get that extra reach you sometimes need, and on alot of the closing birds you are aiming right at them. A good course of action in my mind is to wack in the improved cylinder and get warmed up with that knocking a few birds down and getting comfortable then putting in the modified, i found i couldn't feel the difference between the two except with modified it had that slight extra reach.
Also another not I got told when i got my outlander is that you have to have your head down on the stock and not have it too high, i did this for a while and missed everything that moved hahaa, but once i locked my head to the stock it was great just avoid raising your head when you get excited. on this note to help this i got a i believe it is called ruby red dot? not quite sure if that is it but its identical to the Champion Easy Hit target i have the long red version. and this prevents you seeing any red bead unless your eye is correctly aligned so you dont have to shut an eye it is fantastic! i would definately recommend it!
i use 30gm 6s or 32gms 5s or 6s for the majority of game birds and rabbits etc, no more is necessary and they run smooth as silk through the gun too.