Just from experience and not a professional opinion:
I would recommend a horizontal mulching mower, self propelled, not lesss than 5 horse power and rear bagger. A mulching mower can also be used without the bag and in short growing months (summer)you have no bag to dump or mess with because the blades of cut grass are mulched so fine and blown bacj into the lawn where they benefit the growing grass. Self propelled so you donbt have to push it, just steer. And 5 h.p. so it can power through damp grass and cut it as well.