Keep a round chambered.
After 18 years of war, we found out that Soldiers who carry "cruiser ready" forget to chamber a round more times than not. They squeeze the trigger then nothing. Then freak, chamber a round, then fire. All that takes time, and when under stress, will make you prone to mistakes.
I am also not a fan of letting an intruder hear me rack a shell. It gives away my position and the element of surprise is gone. If I don't know exactly where he is, I am double screwed because now he knows where I am.
The first sound he will hear is the shotgun blast, THEN racking the next round.
If your gun is leaning against a wall, its not going to fire if it simply falls over. If you are worried about that, lay it on the floor just under the bed.
I prefer a #4 or #6 pheasant type load over buckshot. Less sheetrock damage to repair and I really don't want lead going thru multiple walls and hitting one of the kids. Where you are going to work is up close and the energy of the round will degrade quicker with a lighter load but still kill the intruder.
Also, don't think you should go hunting an intruder. If he is in the house downstairs and everyone is upstairs, camp out upstairs with a clear shot at the top of the stairs. Call the cops. If he comes upstairs, blast him. More times than not you will give yourself away making noise trying to track down the perp and he may get the drop on YOU. Lie in ambush, like a snake, preferably a Bushmaster. :)
Teach your kids how to handle a shotgun. I did and both of mine look like Delta operators when hunting.
My $.02.