One of the benefits of competition shooting is that you break everything down about the gun. Everything. Experiment, seek consul, and learn what the fastest way to do "X" is. Take what works and discard what does not. That's why you see 100% of the best shooters in the world shooting in some version of the modern isosceles stance and no one worth mentioning shoots Weaver anymore.
Today we shall discuss how to pick up your handgun. There's basically two schools of thought that work and I'll actually use either one, depending on the stage situation and tactics.
First up, what we'll call the "scoop", it looks something like this:
In the scoop, you basically stab your thumb under the beavertail/backstrap of your pistol and get your fingers under the front strap of the grip, pinching the gun off the table and up into your hand. In the picture above, you can see my index finger is also hooked slightly over the trigger guard.
Another version of the scoop without getting close to the trigger guard would look like this:
It relies more on getting your thumb under the gun and is easier to hit the pistol and either cause it to move along the table or push down hard enough to engage the mag release which will cause your mag to fall out rather unceremoniously after the first shot is fired.
Pluses to the scoop are that it is very natural and instinctive, and easy to do - you really don't have to "learn" anything to do it right; just always be aware of where your trigger finger and middle finger are grabbing and you'll be fine. I've seen folks get in a rush and hit the trigger with both of those fingers which is never a good thing when you're not ready to shoot.
Minuses are that in a hurry, it's easy to grab the trigger if you are not paying attention; it's easy to push to hard and engage the mag release; it's also easy to miss your grip and end up either having to re-grip the gun once you have it in your hands or push it along the table until you get a grip on the pistol.
We'll call the 2nd example the "lift" method. Here's what it looks like:
In this method, your weak hand lifts the pistol slightly using the sights or slide as a contact point. Your strong hand is then free to grab the pistol and get a good grip on the weapon. To do it right, you have to get your weak hand moving slightly ahead of your strong hand, which takes some practice. However, once you get it down, it is (for me anyway), clearly a quicker way to get a good grip on the gun - probably in the line of 2-3 tenths of a second or so. Done right, the "lift" keeps the pistol secure on the table, you won't hit the mag release button and you'll end up with a better grip on the gun than if you were going to do the scoop.
The big minus to the lift is that it is not necessarily instinctive and it takes some practice getting used to. It's also a perishable skill, so if you stop practicing it, you're not going to be very good at it.
If I'm shooting from one position, I will use the "lift" method 100% of the time. However, if I'm grabbing the gun and moving to another position to shoot from, the scoop is often times faster because you can just grab the gun and go - and fix your grip if necessary on the way to the first target.
You might notice that the difference between the two methods described above is only a couple tenths of a second. While on face value, that's not a lot of time, there are plenty of other places in the course of the stage that you can shave tenths off here and there and the next thing you know, you're shooting the stage 2 or 3 seconds faster than the other guy - and as they say, it all adds up!