Because the prompt specifically asked for a book, I went immediately to Amazon and searched the books department for "finding the right pet." No first page results. I decided to google it and go from there.
I changed the wording and googled "choosing the right pet book" and the first choice was Are You the Pet for Me: Choosing the Right Pet for your Family. This book was the only first page result for a book.
Most books on the market were more specific to animals like dogs, horses, cats, etc.