When I started teaching piano, I rotated through different method books, often following the curriculum path I took as a young student. Most piano method books follow similar patterns, so there is no right one to use when starting out a beginning piano student. However, there are pros and cons to each method. Here are a few observations about some of the main methods from my own teaching, and I hope this helps in picking out the right one for your student.
Faber Piano Adventures
Faber’s Piano Adventures is one of the more popular piano method books. The series has four main books for each level, Lesson, Performance, Theory, and Technique and Artistry. One big pro for this method is that the series has many different types of books to go with each level. For example, each level has a Disney book, popular music book, classics book, and many more genres with arrangements specifically for that level.
Alfred
In my experience, Alfred Primer Level method books are very similar to the Faber in difficulty and content. Alfred does also have multiple books per level, each focusing on lesson, theory, and technique like Faber, but has fewer options for supplemental materials matching each lesson book level. However, Alfred does have more options for older beginners as well as a great adult beginner series. Also, Alfred does have more options for intermediate and advanced materials after finishing the basic method books, focusing heavily on classical masterpieces but also incudes pop and other genres.
Suzuki Piano Method
Suzuki Piano Methods is not as straightforward as Alfred or Faber, but it does focus on classical repertoire more than the other two methods. Similar to Suzuki violin, Suzuki piano is traditionally taught with a heavy emphasis in ear training and usually requires a Suzuki certified teacher. This method is a highly successful method but is not as straightforward or inclusive of non-classical genres as Faber and Alfred.
The right answer for which method to use will depend on the teacher, student, and learning goals. For new teachers, Faber is probably the most user-friendly method for young beginners. I would highly recommend the Alfred Adult All in One course for high school and adult beginners. For students who want to jump into serious piano playing or if they have a strong support system at home, Suzuki piano might be a good option too!