So a question that often comes up in numerous gun forums is: What caliber bullet is the best?
Short Answer: The one you can handle the best -- where you have an accurate grouping -- plus, any gun is better than no gun if you find yourself in a situation where you need it.
Long Answer: The one rule of Hand Guns is that "stopping power" is largely a myth. Bad guys are stopped one of two ways - hitting a critical organ (heart, brain, spinal cord), which in the case of the heart could still give the attacker as much as 30 seconds of fight left in them -- or, puncturing enough holes so the attacker bleeds out and passes out from loss of blood pressure.
Compared to rifles and shotguns, all hand guns suck.
But since you can't conceal an AR-15, here's my opinion on some of the various handgun calibers and why I would or wouldn't recommend them for self defense / concealed carry.
First -- just forget about .50 Cal or .44 Magnum. You're not going to find a small frame gun to conceal chambered for these rounds. (No matter how awesome they may be.)
Second -- no matter what caliber, do not carry FMJ (Full Metal Jacket) rounds. In a number of states, Texas included, you are responsible for the round. If it goes all the way through a bad guy and hits an innocent person, you're on the hook. For self-defense, you want a round that's going to hit the bad guy, expand, and stay in them causing as much damage as possible. So buy and carry some form of expanding round. Remington Golden Sabre Hollowpoints are good, so are Federal Hydra-Shoks and Hornady Critical Defense rounds.
Now one to some of the more popular rounds.
.45 ACP -- This is what I carry in my everyday carry gun (a Springfield XDS). I am physically strong enough to more than handle the gun, and the .45 ACP is a heavy, slow round (compared to the 9mm and .40 S & W) but leads the pack in FBI statistics in "one shot stops". For a handgun round, the .45 ACP is a pretty devastating round. However... the recoil can be a bit much, and if you aren't strong enough to reliably control the gun, it's not for you. If you can, .45 is the way to go.
.40 S & W: Sometimes called the .40 slow and weak when compared to it's 10mm sibling, the .40 caliber round is also an effective round. The recoil tends to be a little sharper in pulling up as opposed to the .45 (where the recoil is more of a back push) but some people can handle the .40 better than the .45. It's a good choice.
9mm: The 9mm round is often denigrated, but the fact is I used to carry a 9mm as my everyday carry until I bought my concealable .45. The 9mm is smaller, but faster, than the .45 and the .40, and carrying a hollowpoint round here is even more critical. However, 9mm often takes 2 shots to stop, so if you're going to carry a 9mm (or any other gun, really) practice is very, very important. Double-Tap!
That's it. That's the, uh, unholy trinity of hand gun rounds that I'd recommend.
The rest are too small in my opinion. And no, I especially recommend against a .357 magnum -- it's a small bullet (even smaller than the roughly .38 9mm round) and much, much faster. Even with an expanding round I think the risk of the bullet passing through the target and wreaking havoc on innocents is too great. .380 ACP, .38 Special, .22 -- better than nothing, but unless you hit a vital organ you might just piss the person off.
Home defense? IF you can handle the recoil, get a shotgun. Otherwise, or if you're married, the AR-15 is an excellent choice. Or even better -- get both! I have one of each, as my wife is not physically strong enough to reliably handle the 12 gauge boomstick. The AR-15 on the other hand, has very little recoil (part of why they're so popular) and most women can easily handle it. Plus, most magazines are 30 round capacity (and MagPuls are awesome). The AR-15, despite the claims of our mentally retarded Vice President, is EASIER, not harder, to handle than a shotgun.
For the AR-15, you can buy expanding rounds, typically both Hollowpoint and Softpoint (especially in .223 Remington - but be careful here. If your rifle is not rated for the 5.56x45 NATO rounds, DON'T USE THEM IN YOUR RIFLE. However, if your rifle is rated for 5.56 NATO (like mine is) you can use either 5.56x45 or .223 Remington. The 5.56 round is same bullet, but the 5.56 NATO variety has a lot more powder behind it, meaning a much faster muzzle velocity. For the shotgun -- double-aught buckshot, and maybe for the last one load it with a 1 oz slug. Though be sure of what you're shooting at, that slug may pass through your brick and your neighbor's brick.
Finally -- always aim for center mass. Unless the bad guy has body armor, headshots are stupid. And if you think you can "shoot the gun out of the bad guy's hands"... well, the gene pool is better off without you in it.