Not to add anything that hasn't been said before, but there is no real advantage to having a more expensive round that does not kill birds any deader any further than 2 3/4 or 3" shells. We shoot a pile of geese here, mostly pass shooting which generally is at the end of lethal range, and my 870 with 3" Hevi-metal shells will kill them just fine. The Hevi-metal shells are the only "trick" load I use, being half steel half Hevi-shot so they are around $20/25 which is still in budget. For decoyed geese or ducks I shoot 2 3/4" or sometimes 3" no 2 or BB Estate shells which run $9.99 a box here and will kill things dead as dead gets inside of 35 yards.
There is nothing wrong with any of the shotguns you mention, I prefer 870 pumps because of the conditions we hunt in which can turn an autoloader into a single shot, but if it was also going to be your dove gun, I could see an auto being more ideal.