I think if you have children in your house then a shotgun would be to hard to hide/store safely from the kids and still be easily accesible to you. You can buy a small safe for a handgun that all you have to do is touch the top of it with 4 fingers and it opens. It can be set for 2 different people. That way the handgun would be safe from children and very easy accesible. Face it most times if you need a home defense weapon in a situation,you prob wont have time tohave the ammo and gun seperated or have a trigger lock on it.
If factory ammo is the way your going, then just buy the home defense ammo. It is made to break up very quickly when it hits a target so it doesnt penetrate through walls and such.