Supposing you want to shoot someone who is across the street, that's maybe 50 to 100 feet depending on your neighborhood. If your shotgun load spreads 1 inch per 1 yard, that's a pattern from 15 to 30 inches across. Seems it would be easier to hit someone with such a shotgun load, than with a rifle bullet, if you are of only average skill. I suppose it would be nice to have some sort of sight on the shotgun.
Interesting website on defense ammunition choices for shotguns of different gauges:
http://www.internetarmory.com/shotgun_ammo.htm
Do check out what the local ranges will let you shoot. If you have a shotgun but not a convenient place to practice with it, that's not so useful.
From what I know - which is limited, I've had more experience with handguns - a basic 12 ga or 20 ga pump shotgun seems like a good choice. Cheap, reliable, lethal, intimidating.