So what's the answer? Some call it "gorilla grip." My friend and colleague, Mas Ayoob, dubs it "high hand and crush grip," two of his five key components of successful handgun shooting. Whatever you call it, you should be gripping the gun hard enough that the checkering or markings on the grip are impressed into your hand. You should be gripping it hard enough that your fingers cannot tighten any more, so that there isn't any sympathetic movement of your other fingers as you run your trigger finger. It's called "milking," and it throws your shots low and to the left if you are right handed. If your fingers are already gripping as hard as they can, you won't have that problem. If you're shooting one-handed, or your hands are slippery, you will certainly need a maximum crush grip on your gun. Hopefully you will have the use of your support hand. It needs to be gripping just as hard. The middle knuckle of your support hand index finger should be right up against the underside of the trigger guard and the other fingers should be right together. Don't allow your hand to slip down the back of your gun-hand fingers, toward that cup and saucer grip. If you crush grip with both hands, they will stay together--and so will your shots. Your gun and your hands should be like they are welded together. This will provide the best control of the recoil, the best rapid fire recovery from shot to shot and the best resistance to an attempt to take the gun away from you. And, by the way, your support hand will be far enough forward that you won't be able to accidentally get your thumb behind the slide.
And what about your thumbs? Oh brother, do folks get in a tizzy about this one! Let's try to be logical. The strongest grip is going to be for your thumbs to curl down, with your support thumb "pad" on top of your gun hand thumbnail. Thumbprint over thumbnail, if you will. Some pretty heated arguments have started over whether the thumbs should curl down, point forward, or the thumbs should point up. Some of my colleagues have made a career of advocating one method or another. How about this: do what you need to do to maintain a firm grip. Everyone's hands are different, the grips on the guns are different and the best method is whatever gives you the best control of the gun. For example, some folks who shoot with their thumbs forward do very well. Some, however, constantly hit the slide release (or slide stop, if you prefer) during recoil, locking the slide back. Thumbs forward may be a bad choice for them. Some people with long fingers, or even some medium-sized fingers on small guns (like the J-frame sized revolvers), can't achieve full trigger travel without their support hand thumb impeding the rearward movement of their trigger finger. Again, thumbs forward may not be a good technique in that case. Some people have actually advocated using the thumbs forward as a way of assisting with accuracy, pointing at the target with the thumbs, as it were. Well folks, the little bumpy things on top of the gun are for indexing it on target. And when was the last time you saw anyone naturally point at something with their thumbs? That seems to be a task for your index fingers. Simply put, whatever you do with your thumbs, they need to be supporting your best control of the gun.
Finally, the web of your hand needs to be as high on the back of the grip as you can get it. There should be a little ripple of flesh in the web of your thumb and forefinger as it presses up against the grip tang. This gets the pistol as low in your hand as possible, giving the best alignment of the axis of the bore with the axis of your forearm. This is the firm support an auto-loader needs to function most efficiently. It also minimizes the felt recoil. If you let your hand slide down on the grip, even a little, it acts as a fulcrum to allow the gun to "whipsaw" upward as it recoils and the slide reciprocates. I can't even count the number of people I see do this and then complain about the "nasty recoil." Recoil is what it is. It is how we manage it that determines how it feels. If you have a high, strong grip on the gun, it will function better (you will not have to worry about so-called "limp-wristing"), you will have better shot-to-shot recovery and you will be more accurate. That sounds like a pretty good combination to me.