They all serve a purpose based on where the threat level is currently located. I would say the one “have to have item” is the pistol as it offers the most effective close range defense in the event the threat escalates to that point. Shotgun would be my second choice. Probably using #00 Buck to provide a little more coverage with ample damage to the threat. The drawback is that in close quarters the shotgun is a less maneuverable than the pistol. The rifle, like the shotgun is less maneuverable than the pistol in close quarters. But if living in a more remote/rural setting with ample distance to see the threat approaching this offers the most range to engage the threat before they make it physically closer to you and your dwelling.
Just my thoughts on how all three play a role in defending us.