This site is a great place to start research. It has tips on how to be a good pet owner in general, and then links to how to be a good dog, cat, and exotic pets.  There’s a section where you can send in questions and read his previous articles.

This site goes over the big questions you should ask before committing to a pet and why each question is important.  It also offers links to picking specific animals, such as dogs, cats, birds, and exotics.

Coming from a parent’s perspective, this article goes over the main things families need to think about before owning a pet, and where proprieties need to lie once the animal(s) are settled in their new home.

Once again, this site goes over the main questions to ask before adopting a pet, including what to do if someone has allergies to animal dander and what pets would be best for those families.

While this site is not as extensive as the others, it is easy for children to follow.  It offers basic advice on how to raise your animals.