-Carry a weapon or be defenseless.
-Carry the deadliest thing you can carry.
If you choose to carry a gun:
-Carry the most powerful caliber you can carry if you choose to carry a gun. When you are talking about handgun rounds and their various designs what this really means can get confusing.
Just step back and think about what actually stops somebody. Head shots are indeed great. But people misunderstand why they are great. Pretty much if you damage any part of the bad guy's brain it is bad news for him. The cerebrum is responsible for thinking and movement and it is the largest part of the brain. But you have to destroy a large portion of it if not all of it in order for the bad guy to stop moving instantly. And aiming for the cerebrum requires you to aim for the more angled portion of the skull and it leaves the lower brain intact to control the body and perhaps permit the attacker to fire their gun again via reflex or some similar action.
It has already been discussed that severing the spinal cord anywhere from the neck all the way to the top of the medulla oblongata will obviously cut the brain off from being able to control the rest of the body and will instantly stop the attacker. However that requires you to aim for the nose (if the bad guy is directly facing you and is looking straight at you). Or if the bad guy is looking to the left or right that will require you to aim for the ear canal. And on and on for all of the other orientations of the brain. On top of that it is a really small target located behind the tough, angled skull.
So pretty much if you do choose to shoot someone in the head you might as well pick a round that can penetrate the skull at as many angles as possible and destroy as much of the brain as possible. That is you can even effectively conceal a hand gun that carries that kind of caliber.
This is pretty much why you want to aim for the center of mass because it is hard to do things when you can't breathe (lungs are collapsed from gun shots... and they are bigger, less armored targets than the brain). Don't count on a heart shot either. The brain and the rest of the body can live for several minutes without fresh blood. It takes sixty seconds to bleed out from an artery and you pretty much won't bleed out if the heart is destroyed... you will leak out. Either way it will be a while before you absolutely must stop (assuming you don't go unconscious or are consumed by the pain... you know... drugs and/or adrenaline can make you pretty tough).
All of these things facts show why all of these "extraordinary" events occur. Basically, you need to have as many rounds as possible. Whatever you can carry. We can't always count on getting a clean shot on a target as small as the head under stress. We need to choose a round that can penetrate as deeply as possible through the torso. The only thing we can really hope to accomplish with pistol calibers is massive trauma to as many organs in the torso as possible... this will make it hard to breathe (lungs) and hopefully induce shock so we don't have to wait for them to bleed to death. Unfortunately drugs/adrenaline can make people immune to pain and thus shock. So I would pack as many rounds as possible that can penetrate as deeply as possible that can ALSO penetrate the skull reliably (as hopefully after half the mag the bad guy will at least slow down enough for you to stop them with a well-placed head shot). That is my plan. I believe THAT is the most effective way to choose a caliber. Whatever cartridge you pick as long as you can do that I believe you will be able to stop any attacker you will face in a self-defense scenario.
Don't plan on one well placed head shot (or trying to hit the head once or twice with your whole mag). Don't plan on one-shot-stops. Don't plan on never missing or missing very little. Don't think any round will compensate for accuracy, training, and shot placement. Pick the round you must based upon what you are able to carry realistically. Analyze your round of choice's capabilities and train to maximize its strengths in a self-defense situation. Understand that a .25 or .380 might not reliably penetrate the skull. Realize that a 9mm or a .45 might not penetrate the skull either. Realize that handguns suck at killing. Realize that you will miss. Realize that there is no one round that will do the job. Pick the one that works best for you in your situation and train to use its strengths to the fullest extent.
-Whatever gun you choose to carry make sure you train with it.
-Make sure you can actually hit with what you choose to carry.
-Make sure you can actually conceal what you choose to carry. The clothes you normally wear, your daily routine, the time of the year, et cetera all determine the size of the weapon you are capable of carrying without letting everyone know that you are armed. The size of the weapon limits the capacity and/or caliber of the weapon you choose to carry.
I wrote a lot. Sorry.