If you have a dog, make sure that your yard is fenced and gated to prevent it from escaping. Too many dogs are killed by running into the street and getting hit by a car. Of course if you have a cat that goes in and out, it will probably do a certain amount of wandering. But they can get into someone's garage, get hit by car, etc. When it comes to your home, keep in mind that puppies and kittens are especially curious.
Puppies like to chew on things and kittens get into things.
It is important to take your new pet to a veterinarian on a regular basis. Fortunately, animal care is the very best in Southern California so you shouldn't have trouble finding one to your liking. Make sure you keep your pet current on shots and immunizations. Seriously consider having your pet spayed or neutered. Adding more would just deepen the tragedy.