Moderators/Admins, can we get this moved to "Selecting a Handgun"?
To the OP:
Welcome to the forums!
What caliber and type of handgun you choose depends on what you're comfortable with using. Almost all self-defense loads involve a bullet with a hollow point, which causes the bullet to expand easier compared to a standard full metal jacket. Basically this means when you hit something with the bullet, the bullet 'pancakes' and loses a lot of energy going through the target or stays in the target due to lack of energy. All bullet types do this but hollow points (and some other bullet types) mushroom at a much greater rate than traditional jacketed bullets.
It primarily depends on the load of the round in question. Hot loads (more propellant) will have greater pressure and thus greater velocity, making for a better overall range and accuracy, but more likely to overpenetrate a target. I use a custom load of 4 grains of bullseye powder behind a 124 grain Nosler JHP bullet and I'm not sure what the velocity is at, but it's definitely lower than my factory target loads - which are 110 grain FMJ with an unknown quantity of propellant. However, it won't compete with a .45ACP round with a hollow point because the .45ACP is already almost .10cal greater in diameter than the 9mm. In addition, the standard velocity for most .45ACP loads is much less than 9mm.
If it were just comparing FMJ in 9mm and .45ACP, I'd go for the .45 every time. The footprint of a .45 and the lower velocity have a much greater impact than a smaller 9mm hole going clean through. However, unlike the military, we aren't required to use FMJ bullets and so the bullets we can choose to use can make the 9mm quite competetive with the .45ACP.
Personally, I've shot a deer with a 7.62x39mm hollow point round which broke it's back and shattered the bullet - pretty much because the hollow point hit a very hard load bearing structure. It did a lot of damage and didn't overpenetrate. The same would probably have been true if I'd used a FMJ. I won't delve into that too much as I don't want to gross people out.
I've had experience using 9mm elsewhere, but I'm not going to talk about them here (due in part to certain idiotic legeslation passed earlier this year, and in part to not gross people out or otherwise make myself look bad). But needless to say, if you hit a living creature with a 9mm hollow point in the right place, they *will* go down.
One last thing: .45ACP takes a lot more practice to be used effectively versus 9mm. The first .45 I tried, I was hitting the bottom of the target with it. The first 9mm I used, I hit a 4" square area with the whole magazine. So if you do go with .45cal, be prepared to get a lot of practice.
DAO means double action only. Basically, every trigger pull requires the same amount of force. In a traditional double action (DA) - and someone correct me if I'm wrong - the first shot without the hammer cocked will require more force, but subsequent trigger pulls will require much less force. In single action (SA or SAO), you have to cock the hammer in order to fire. It can be likened to what the trigger does - in a double action, it cocks the hammer and releases it (two actions), in a single action it only releases the hammer.
Now, there's a lot of handguns chambered in .45ACP out there. There's the classic 1911 series, of which are quite abundant and relatively easy to acquire for a fair price. They are traditionally single action only, but I'm sure there's some out there built with double action capability. I'm no expert there, so I'll let someone handle that.
My personal preference would yield toward some of the european designs out there. Those would include the SIG P220, H&K USP, CZ97, and FN FNP-45. I've never tried any of these out, but maybe someday I'll get to. I don't really like the DAO designs, but they include the Glock 21, 30, and 36; and Ruger P97, to name a few.