Here's an experienced fellow's point of view.
Carry/use the biggest caliber you can reasonably control at a sustained rate of fire. Learned that from
Massad Ayoob, who taught my instructors...and whom I hope to learn more from someday.
12ga is great for the home. As stated before, a proper lock negates the 'need' for a gun safe. However, when leaving for extended periods of time, it's nice to have something really secure to store it in. I've known a few people who had houses broken into, but guns were left alone because they were properly stored. I don't know about you, but if someone steals my TV I don't really have to worry about them committing a crime with it.
Also, CONTRARY to what was stated, the 'racking the slide' is pure Hollywood. Sure it's a recognizable sound to a sober person, but someone under the influence may not react the way you want them to. To ME a racked slide means one less shell loaded in the shotty. One simple way to handle things is to assess where the family is, and get on the opposite side of the bed from the door, lay the shotgun across the bed, and STAY PUT. You may know your house, but your bed is going to be some of the best cover you have. Keep a phone next to the bed and get everyone to that side. Have extra shells handy on that side of the bed, along with a GOOD flashlight. Holler out that the police are on their way and to stay away from that room, or there'll be hell to pay. Does this make sense? STAY PUT and call the police. DEFEND yourself, not your property. Material things can be replaced, human lives can't.
As for hardware you don't have to worry about having a 'short' barrel if you stay put in your room. Shorties are for room to room clearing, which would only be required in a special situation...such as running to the kids' room to grab them. If you can assess that they're OK then watch the hall. Pistols work well for all situations. I prefer 12ga for home use because of the multiple projectiles and greater probability of hitting and area target.
ABOVE ALL I highly suggest receiving some training not only in marksmanship/tactics, but in state laws. Just because you may not be carrying concealed, you still need to know how your state views home defense. REALLY consider that just because someone enters your home, you are not obligated to blow them away. As I said earlier, material items can be replaced...so defend YOURSELF and FAMILY first. A crackhead with a DVD player in hand is typically not considered a threat to your safety. Understand that while there may not be any legal implications to a defense situation, there are certainly civil ones involved. In other words, you may not have charges filed against you, but the deceased may have left family behind who will likely sue you for civil damages. Having a full knowledge of these implications and a lawyer on retainer sure help you sleep better at night.
Take this all for what it's worth, as I can't make you follow everything I've stated. I am speaking from experience and will be happy to answer any questions you have, Billy. My door is open. I can go through my channels to put you in touch with folks in your area who can help.
Lemme know and I'll give you a call sometime.