One of the important rules of safety in Gun Training for self defense or in just target shooting is to be sure of your target and what is beyond. You are responsible for the bullet from the time it leaves the gun until it comes to its final resting point. When plinking or target shooting a backstop is needed so that your bullet will not go beyond its intended destination, like at the indoor range, or outdoors where their is a large hill or mound of dirt called a berm. Most times when target shooting people use FMJ Full metal jacket ammo or ball ammo. This ammo has a lot of penetration great for target practice but maybe not so good for personal protection. The new personal protection rounds that are on the market now are for that personal protection scenario where what is beyond your target may be another person or a crowd of people. It could even be a wall to another room where children or family are sleeping. These bullets are designed not to over penetrate their destination by breaking up or distorting and loosing their energy after they hit the intended target. Here is a video showing these type of rounds in use
I recommend that you use standard personal protection ammo that police officers most often use. Federal Hydra Shok, Speer Gold Dot, or Federal HST
Talk to the experts at the gun shops about all these types of rounds. While they are more expensive than regular target ammo, these rounds definitely have there place in your arsenal for self protection.