I think most new students, nowadays, start out with Suzuki books. Personally, I am nit fond of the system and if your teacher is not a SuzukiTrained instructor, chances are, the Suzuki method, itself, is not being used, just the books. That is not a rule, but pretty much the case. The system is meant to be taught using the system. I believe authorized Suzuki teachers take a course to be certified, but not positive.
I find the order the sings are presented, often times, does not make sense. I have heard others say the same thing. The books, themselves, do not provide much instruction, the Suzuki Instructor fills in the “how-to’s”. These are difficult for a self-learner to learn from.
That said, the books, themselves, as an addition to lesson books, add a great variety of songs at different levels foe you to learn from. Just find songs that fit where you are at, and add them to your repertoire. I love most of the songs. You will find that some of the same songs appear in different level books. That is because the next level has a more advanced playing arrangement, ie “Long Long Ago” is in book 1 and Book 2.
These are my opinions, other Suzuki Books users may have different opinions and uses.
The Bumble Bee Flies