What is your budget? If you will be using it only for deer you can buy shotgun set-ups specifically for deer (rifled barrel with cantilevered scope mounts. And then you can always buy other barrels to tke you into a variety of other shooting sports....squirrel, rabbits, pheasants, grouse, dove........you name it.
The Mossberg 500 has a few packages for deer and some combo packages as well. The Remington 870 is a little bit more costly but more people seem to prefer the Remington.
You could probably find a used shotgun with all the trimmings for a decent price. I'd get one with 3 1/2 " capability for added versatility.