Go to a range/store that rents various handguns and try them out. While at the range, take a handguns basics class and try to understand what tool you need to get the job done.
Smaller hands doesn't equal smaller firearms. The smaller and lighter the firearm is, the more recoil it has and the more difficult it is to control with small hands.
If you do not plan to carry the handgun concealed, consider a larger model that has higher capacity and weight. My recommendation would be a 9mm Glock 19, a 9mm Glock 17 or a .45 ACP Glock 21.
Make sure to seek training. While training classes may initially seem expensive to you, they are worth the money. You will learn when and how to use the firearm, how to maintain it, how to store it in a reasonable way (i.e., loaded and locked away when not at home), and its limitations. Inform yourself about your state laws regarding lawful self defense using lethal force.
Make sure to practice regularly. Become a member of a gun range and visit it at least once a month, shooting 100-300 rounds with every visit. While at a training class, you learn a lot of new things. Practice is meant to exercise and master what you have learned, such that when the need arises, you have the skills. Stock up on practice ammunition by purchasing in bulk.
Lastly, understand that handguns are rather inefficient firearms when it comes to stopping a threat. Shotguns and rifles have significantly better stopping power, i.e., capability to incapacitate a threat.