As subjective as your question is, so are the answers you’re likely to receive.
Take a trip to the gun shop and see if they have an indoor range with rentals you can try out. Its important to first choose a gun you can fire reasonably well. As a small person, you will need to assess your priorities and make adjustments to your dress code, etc. I know because I’m on the smaller side as a man, so I have to choose carefully for the same reasons.
BTW: There are purses that are specifically designed with a special compartment for a gun. Unfortunately, these are rather conservative looking' and may not fit your younger life-style. Still, there are dozens of options so take your time and experiment.