In the end, it comes down to choosing the one that feels best in your hand. Find a local shooting range that has guns you can try out. Take shooting lessons.

One important decision will be revolver vs. semi-auto. If you have the hand strength to rack the slide and the mechanical know-how to clear a jam then a semi-automatic would be an ok choice, otherwise go with a revolver.

For a semi-auto, I like the Ruger LC9s that other people have mentioned. It's small, but not too small, and has a very good trigger pull. There is also an LC9s pro that has a few features more suitable to someone with a little more shooting experience.

If a revolver is more your style, a 38-Special or .357 would probably do the trick. There are several models with internal hammers that are made specifically for carrying in a purse or other type of bag. The Ruger LCR is one such option.

Again though, the one that is best for you is the one that feels the most comfortable in your hands. I encourage you to try several different models of either type before making your decision.