What kind of hunting do you do? heavy cover or open fields? deer? A few more details will help with recommendations.

A 44 in a 14" tube will reach a good bit farther (100+yards) then most people will consider shooting open sights. They often get scoped with a fixed low (2-4) power scope. A red-dot sight is a nice upgrade from iron sights and can be smaller then a scope. A peep sight would work, but I think you would be missing out on a fair amount of the performance in the platform.