To the OP's original question:

Ideally, three lines of defense for home protection:

1) A security system to alert you and police of an intrusion, and deter intruders.

2) A medium-to-large, loud dog(s) with a protective instinct to alert you of an intrusion, and deter intruders.

3) You, armed and having rehearsed likely scenarios.

As far as which weapon, there is no perfect platform, only a series of compromises based on a series of variables.

How large the home, condo or apartment? How narrow or wide the passages? How many points of entrance? How many inhabitants? Are there acres between you and the neighbors, or are there homes on all sides, or families living above, below and on either side separated only by thin walls, floors and ceilings?

As a rule, any round that will penetrate deeply enough to do damage will go through walls, doors, etc., and possibly people you weren't intending it to, so unless you live alone in a rural place there's always that risk. But what a .44 Magnum round nose will go through versus a .38 Special hollow point are two very different things, whether you hit the target or not.

Given that shot placement has more to do with stopping a threat than caliber does, I think smaller, more controllable calibers on a trusted platform paired with quality defensive ammo is the best compromise between power, user friendliness and the risks of extreme overpenetration. I like .38 Special and 9mm with proven hollow points (with an admitted weakness sometimes for .45 ACP).

This means, of course, that in the debate between shotguns and handguns for home defense, I prefer handguns. This doesn't means that shotguns aren't excellent tools and viable for self defense, they are both. I simply prefer the capacity, maneuverability and easier realoadability of a handgun for home use.

At home defense distances, a shotgun's spread offers no meaningful advantage, has limited capacity and is difficult to reload in a self defense situation compared to a handgun; it's also more cumbersome in tight spaces, moving loved ones, carrying children or using the phone.

Does the shotgun generally hit harder? From .410 bore to 12 gauge, using buckshot, you bet. But I'll trade that for the advantages of a handgun in a close-quarters, non-combat situation.

Your question is a good one, and also a can of worms. There are no perfect solutions, but many options, and an endless amount of opinions, most valid, some quite impassioned.

Read a lot, think a lot, draw your own conclusions and put your plan in place.