Choosing the best piano book for beginners can be difficult if you're just starting out. From the books that I've taught, I have one stand-out favorite. I also have some others that I highly recommend.
For Adults: Adult Piano Adventures All-In-One (Faber and Faber). Teaches the notes using interesting songs and moves at a good pace. Good for learning the basics and for moving on to classical or contemporary (i.e.. pop/rock) music.
For Kids: Piano Adventures Primer Level: Lesson Book (Faber and Faber) and Piano Adventures Primer Level: Theory Book. The piano pieces are fun and interesting. I always recommend a theory book to go along with the lesson book. It's necessary for a strong foundation. This book teaches the basics well and at a good pace.
(it's also pretty good)
For Adults: Alfred's Basic Adults All-in-One Piano Course. Teaches the basics in a well laid-out manner and at a good pace.
For Adults who want to learn jazz or rock: Alfred's Jazz/Rock Course. I haven't taught this book but it may be worth looking into if you are only interested in playing jazz.
For Kids: Alfred's Lesson Book Level 1A and Alfred's Theory Book Level 1A. Teaches the basics well and at a good pace. The theory book is a must and one of the best out there. Colourful pictures and fun songs.
Any of these books will start you off with a good foundation. It's important to try a really understand and master the concepts the book you choose right from the beginning. There is a bit of a learning curve but any good teacher will make it fun and enjoyable.
And remember, you can buy the best beginner piano book in the world but you must practice to really get it's full benefit!