If you want real stopping power get away from wimpy handgun calibers. There is an option that comes mounted in a handgun platform, but it gets sneered at.
5.57mm (.224 cal) slices through bullet-resistant vests and will chip away ceramic plates enough to let a bullet get inside. 1,600 FPS+ and 330+ ft/lb of energy. The vaunted .44 Mag and .500S&W might, maybe, do that some of the time.
The bullet does not expand so much as it shatters, creating a wound cavern as opposed to a would cavity - much like the 5.56mm/.223 cal round coming out of the highly recommended for self/home defense poodle shooter.
Google for recent information about the comparison of the various self defense calibers - they all meet the FBI's 12-inch penetration standard and the temporary would cavity does not vary that much between calibers.
"Stopping power" is based on two factors - the stopping of bodily functions that support aggressive behavior (disrupting the CNS for a "drop right there" effect or the rapid leading of essential bodily fluids for a "pretty much done for by 10 minutes) or achieving a psychological surrender. There are those that add a pelvic girdle shot, but that just puts the body down without really interfering with aggressive behavior. Some folks psychologically surrender when they see a gun-like object pointed at them, while some folks keep on fighting for 10-15 seconds after having their heart blown into tiny shreds.
Pick a caliber that you like and learn how to place it in an appropriate spot time after time after time. Sometimes that means choosing a caliber that does not begin with "4" because of the ability to handle the handgun better, and sometimes it means choosing a caliber that does not begin with "4" because you are happier cramming a few more rounds in the magazine.
stay safe.
