Uh-oh. Now you've gone and done it. Start asking about what caliber to get for a concealed carry gun. Here comes the debate!
There are those who will go on about "stopping power" and advocate for the biggest caliber you can comfortably conceal, carry and shoot. And I believe there is indeed something to be said for that. If you are able to hit the target right where you want to hit it, it is best to hit it with the most powerful round you can. After all, the purpose is to stop the threat, preferably as quickly as possible and with as few rounds fired as possible.
But then the more important aspect is shot placement. What's more important than carrying a big thunderstick is being able to place the round right where you want it. If you can consistently place the round within 1/2" of where you were expecting it to go, then the caliber matters less. If you can put a .22 right above the bridge of the perp's nose, he's going down, period. It doesn't need to be a .45 hollow point.
There is something to be said for carrying a lightweight, low-caliber gun. It's lighter and therefore more comfortable to carry, smaller and easier to conceal, and often will hold more rounds, because the ammunition is smaller. And the ammo is cheaper.
Ultimately, you need to hold a few different guns in your hand. See which fits your hand best and feels good. Shoot a few different ones - borrow some friend's guns, or go to a commercial range and rent some. Most commercial ranges have guns for rent so you can try out various ones. Find out which ones you are better with. You might find a cute little .380 that feels comfy in your hand and fits neatly in a pocket or something, but then you might find you can't hit the side of a barn with it and the slide cuts your thumb every time you shoot it. I had that experience with a Beretta Tomcat. I thought it was really sweet, but after shooting it a few times at the range, I realized my hands were just way too big for it and I hated it. I dumped it quick.
It's really a matter of personal preference. Don't let anyone tell you that you need to carry a .45 or anything - find what works for you. When it comes to defending yourself, the best gun is the one you have. Better to have a small .380 or something than nothing at all. As to whether a 9 mm is better than a .380 but not as good as a .40, or whether a .45 is the best of all, I'll leave that to all the chest-thumpers who evidently are happy to argue that ad nauseam in all the gun forums.
Full disclosure: my favorite concealed carry handgun is a Para OPS .45, loaded with Speer Gold Dot HPs.
"[The swords of the militia], and every terrible implement of the soldier, are the birthright of an American."