Glock with a tactical light is what I recommend.
Shotgun takes two hands. If you have to open a door, control a child, be on the phone with 911, turn on a light, etc., you have one-handed a moment when it is out of control, and, perhaps, more vulnerable to being snatched by a lurking perp.
A handgun can be kept close to the body where it is better under control in a physical confrontation. Shotgun is risky in that regard because its length makes it vulnerable when in the “ready” position.
Tac light on a Glock can be activited with the trigger finger, flashed on and off, or simply turned on or off, all while your weak hand is free to do whatever.
I mention Glock, but other pistol/tac light combos probably work the same way.
I just stepped off the longest distance in my house that I can see in a straight line. Bedroom-living room-dining room-entrance hallway from garage. That distance is 34 yards. I have a large dog so I don't expect to be surprised. I have a handgun and can pick rifle or shotgun to sling across my chest depending on what the commotion sounds like. I have motion sensor night lights scattered throughout the house that will illuminate things as long as power is on. I should get a tactical light for my handgun.
We have enough light coming in that I don’t need a flashlight. I DO have a laser on my .38sp. Also 2 fully loaded 9mm in the safe…..