I think a 20 gauge slug gun is more than adequate for whitetails as it throws a slug of about 350 grains or so. By all means, get one with a rifled barrel and shoot saboted slugs. A low end variable scope of perhaps 1-4X is also a wise idea. Besides pumps, there are also some reasonably priced bolt action slug guns available.
For accuracy, either the barrel must be fixed in the receiver or the barrel must have a cantilever mount attached.
Recoil: When sighting in or practicing, place a five-pound bag of shot between the stock and your shoulder. When hunting, you're wearing heavy clothes, firing from field positions and hopefully, one or two rounds at most so recoil should not be a factor when firing at game.