I'd go with a pump for a multi purpose gun. You'll buy other guns for specific uses later, but a pump is the best way to get going.
Assuming you are at least average in size and weight with some firearms experience, I'd go with a 12 Ga. If you are lighter and perhaps more sensitive to recoil, get a 20 Ga. Don't worry about having enough power for deer. The newer 20 Ga ammo will get the job done.
I agree with the others that a combo (gun that comes with slug and field barrels) is the way to go. A slug barrel with cantilever scope mount is the best option. However, if you all you can find is a smooth bore slug barrel with rifle sights, this can work very well for you out to 75-100 yds. My Mossberg 500 with the smooth bore slug barrel will shoot most brands of rifled slugs well enough to kill deer at 75 yds no problem. And, these slugs are way less expensive that sabot slugs.