I started out hunting deer with just a shotgun, they knock em down...nothing wrong with Shotguns. I still hunt with one.

IF you are planning on all of them (Deer, Waterfowl), you could go with a remington 870 with a smooth bore and do all types of hunting with that. Just use rifled slugs. Then if you decide you like it, and want to upgrade a little, you could either get a rifle, or buy a cantilever barrel for the 870, thats what I use and love it.