Pets can be a great way to teach a child the responsibility of taking care of a living organism. However, depending on the age of the child, many types of pets would not be suiting for kids under 13. While many parents thing that getting a bunny or a hamster would be a good idea for their kid, I will have to argue otherwise. Bunnies are cute and fluffy, but they require extensive care that many kids would not be able to fulfill. Also smaller animals like bunnies, hamsters and others are extremely fragile, and can be injured easily from mishandling. While reptiles are a bit of a safer option, they require specific light setups as well as controlled temperature and humidity for many species. Failure to balance all those factors can lead to variety of diseases that will seriously affect their lives.
With that being said, a dog or a fish would be the perfect first pet for a child. Dogs are not quite as fragile, given a bit more room for an error. And fish is relatively easy to take care of. Obviously both of those options have to be under adult supervision.