As far as pump shotgun of choice... I'm gonna be a bit different than the guys here and say Ithaca 37. Well made, smooth loading (no spring loaded shell lifter unlike the 870), smooth pumping, bottom ejecting, barrel securely attached by interrupted thread as opposed to slip fit. New ones probably aren't going to be in your budget. But there's plenty of used ones.
Only downside is older models will be a mix of capabilities. Really old ones (pre 855000 serial) won't interchange with new style barrels. Most will be 2.75" chamber unless you get a Magnum marked one or one made after 1987 (either an Ithaca 87 or a later model 37). Older ones tend to be fixed choke as well.