As a teacher, I have talked with several parents who are home-schooling their children about the best ways to introduce counting. Over the years, I've found a few books that I enjoy, and now there are newer resources that I feel good recommending to parents planning home-school lessons.
The Crazy Birthday Candle Jungle book series by Mark Schmidt is a clever way to introduce and teach counting to children. The series has a book for each basic number and uses clever rhymes, fun language and colorful illustrations to keep children engaged. I would use this book when working with children just beginning to start counting as a read-aloud book and/or as a way to integrate language arts into the math curriculum. Further, the card games allow the children to continue to develop their math skills without realizing that they are completing work.
I would rank this book in between a basic counting book and a more advanced math story. Some other notable books that could work in a similar role are listed below:
Olivia Counts by Ian Falconer
How Do Dinosaurs Count to Ten? by Jane Yolen
Fish Eyes: A Book You Can Count On by Lois Elhert