First thing to do before deciding on caliber or brand is to get training. Once you know how to shoot a handgun, go to a range that rents them and shoot as many different types as you can. Once you learn the different types of actions and calibers, you can narrow down the choices from a thousand or so down to a more manageable level. Just knowing whether or not you want a revolver or semi-automatic would help a lot, but it appears that you do not know this.
9mm, 10mm, .40S&W, .44special, .45acp, +p.38special, .357 magnum are all fine for defense use. Even the larger .41 and .44mags would be fine as long as you tailor the load to your needs (some of these loads are more suitable for hunting). Within these calibers are many, many hundreds of handgun choices....