Stopping power does not exist. You can shoot a guy with a .45ACP and he might not go down. While a 9mm with proper shot placement could stop a thread instantly. A 9mm is cheaper to shoot on average, has more manageable recoil, and generally is better for a first timer to get used to. It has enough muscle in a good JHP load to get the job done provided you can put the shots on target. I carry a .40SW because I wanted something bigger than a 9mm while keeping the same relative frame size for the gun. That meant that .45ACP was out and I really decided against carrying a high dollar 1911.
My recommendation is go for 9mm.