Many wonderful suggestions from everyone...
I would add a few minor suggestions that might help...
1) You might want to stay away from a pistol grip with no stock. Sure, they look mean, but they require quite a bit of training and practice to use effectively.
2) The shorter the barrel, the wider the dispersal pattern (for the most part). Most states allow a barrel length as short as 18.75".
3) Other conditions might affect your choice of weapon, barrel length and ammunition: Do you have children in the home? Someone who sleeps in the same room or another room? How is your home laid out? Do you have long, narrow fields of fire (hallways), or lots of open space with few walls? Where are your blindspots from each of your firing positions? What will be in the background (windows, deflecting surfaces, etc) of each shot?
4) Practice, practice practice. The safety course you mentioned is a must, but won't do you much good if you never practice the fundamentals. Do lots of range time to become comfortable with the weapon. If you can, do UNLOADED scenario walkthroughs in your home. (What would I do if he/they came in here? or here? What if I were in this room? Or this room?) I recommend that the weapon remain unloaded and that no one else be present in the home when you do these walkthroughs.
These are all things you need to completely address BEFORE a situation happens. If the day ever comes where you need to defend your home, HOW you do it should already be second nature.
Weaver and Ayoob have both written excellent books on combat handgunning and shotgunning. Look for all the information you can find from the very few reputable authors who have actually survived armed situations.
...and, at the end of the day, keep it as simple as possible. The situation for which you're planning is incredibly stressful, and you will be very afraid. The physical and emotional elements will be hard enough to overcome. The fewer moving parts you've got in your equipment and your plans, the better chance you'll have of successfully eliminating the threat.
Something to think about with these bad-boy combat and pistol-grip shotguns is that if you ever have cause to use one, and you're being harangued by some overzealous, anti-home-defense prosecutor, that's the gun they'll be showing in a courtroom.
For that reason I'd rather have something that looks less "intimidating", like a plain-Jane Rem 870 Express with walnut stocks (owned one before and am thinking about getting another after last week's events in N.O.).
Amen - under stress most people can't hit with them and everybody with them thinks they can. Besides that it is freaking DISCO.