If you are looking for a first handgun for a woman, you have a lot of choices. To make a good decision you have to know what you are planning to use it for.
If you are looking for an everyday carry gun (EDC), weight and size is going to be a consideration. You will want something smaller, that is easy to carry. Remember if you it is inconvenient you (or your lady) will find excuses to leave it behind.
Now when you go lightweight, you are giving up control and potentially accuracy. A good gun for the home might be heavier. Recoil will be less and you might be able to get a better grip on a bigger frame gun.
Check out this video for a couple more considerations. Let us know what else a woman should look for in her first gun.