Barrel length is a personal choice and can change from gun to gun , from o/u, auto ,pump. Shoot was fits and feels good in your hands, that pretty much sums up barrel length.
The length has absolutely nothing to do with how a shotgun will pattern. That will be determined by forcing cone, back boring (if any) and choke.
The only way to really decide whch choke/load is right in any particular shotgun is to spend some time patterning.