The only type of ammo which is useful for self defense is buckshot. Either 00 or 000. Both will penetrate more and further than 5.56. Using birdshot is likely to be ineffective, and in some instances could bring charges for 'maiming' since birdshot is not intended for engaging anything but... birds.
Protecting oneself requires using tools that are effective. Anything which is effective won't be stopped by interior doors and walls. Bullets exiting homes are rare. Being in control of where you have to engage a threat from is the way to avoid unintended hits. The only way to 100% eliminate projectiles is to rely on non-projectile means of defense. As a result, what's best for each person varies.