One of the biggest mistakes I see with women shooters, especially new ones, is a fear to take control of their gun. Having a gun that fits properly is just the first step; proper grip is the second. YouTube is full of videos mocking women shooters who have hit themselves in the head with whichever handgun their "friends" have given them to shoot. Those videos infuriate me for one reason - with proper instruction, no one would ever get tattoo'd by their handgun.
Proper grip will allow you to control the recoil and bring the gun back on target much more quickly, which means you can get your next shot off much more quickly.
Attitude is crucial when handling guns. If you are afraid of it, or of the recoil, it will bite you. Tara's favorite phrase when dealing with new shooter is, "Hold it like you own it, not like it owns you." You control the gun, not the other way around.
A good grip starts the same way you check for fit, with the gun snugged into the web between your thumb and first finger. Your index finger should rest along the frame of the gun, the other fingers wrapped comfortably around the grip. Your support hand should be wrapped around the gun, covering the fingers of your strong hand, both thumbs facing forward.
Having your support hand wrapped around your strong hand helps control muzzle flip - when the gun fires, the front end of the muzzle will "flip" up. Not controlling the muzzle flip is what caused all those women in the YouTube videos to smack themselves in the head.
It used to be popular to support the gun in a "tea cup" grip, with the support hand cupped underneath the gun, like a saucer under a tea cup. The problem is that the gun can flip up off of the "saucer", leaving the strong hand to control the gun and bring it back down on target. In order to avoid that from happening, people who use the tea cup grip will hold on tightly to their strong hand and pull down, which can cause their shots to dive.
Thumb position is very important when shooting a semi-automatic. Semi-automatics are designed so that when they fire, the slide is forced backward, ejecting the fired brass and reloading a new cartridge. If your support thumb is wrapped around the back of the gun the slide will take off skin when it cycles. It hurts. A lot. Trust me on this one. Keep those thumbs out of the way.
Having the gun tucked into the web of your hand will direct recoil back through your wrist, through your arm and into your body. Absorbing the recoil with your body instead of your thumb (as with a poorly fitting gun) will make shooting even the biggest gun a lot more fun.
Here's a slow-motion video of me shooting; watch the muzzle flip up and notice how my grip helps to bring the gun back down on target so I can get the next shot off. Thanks to my flabby, out of shape arms, you'll also be able to see the recoil travel from the gun to my body.
Now here's the same clip at "normal" speed. In slow-mo, the muzzle flipped looked huge, but in this clip it's minimal. You can also see how my support hand balances out the upward movement of the gun, simply by resisting the movement. I don't have to muscle it down like I would if I used a tea cup grip.