Yeah, get one of the combo two-barrel setups from Rem or Mossberg and you're all set. You can also pick up a used regular-type shotgun and then purchase a deer/slug barrel separately. Just about all pumps and semis had that as a option.
Yes, sharptail is mostly correct - one shotgun does not EXCEL at everything but you can get one which will at least function in all those instances. As you try each form of hunting, you'll find whether you prefer grouse, ducks, geese, clays, or deer. Then you can branch off and get a shotgun to specialise in that area. But you have to start somewhere, and this is as good a compromise as you'll find.