Thanks for the note with your question… That helps a lot hearing about your previous background as it relates to piano. You are far from being alone! Let me take a crack at answering each our your questions:
“Will the music books that accompany the lessons provide the underlying music theory and the complete musical notation (in addition to the kind of abbreviated notation you reference in your advertising)?”
Yes – and no. As to the theory behind how we play in the styles we do, absolutely yes. And that occurs not exclusively in the books by any means, but also in depth in the lessons you will be watching that are tied closely to the books. Keep in mind I had the luxury when developing this online learning environment to develop the lessons I teach and the course materials in a tightly integrated manner. Neither is sufficient by itself, but with both (I am constantly discussing, expanding upon, and referring to the books during the lessons) it is turning out to be a pretty unbeatable “one-two punch” if you will. I’m just stressing that because from your question it kind of sounded like you might be thinking the books are more important than the video instruction, which is not the case. If all you will have access to is the books, I am probably not a good fit. You absolutely need (and want) both as you work through the Courses.
Now as to the clear “no” to your question … The written notation we use throughout the 6 Course Books and the 3 Music Books is exclusively in Lead Sheet format. You will never find traditional classical notation (i.e. Grand Staff with both Bass and Treble Clef) used. I know it might be hard for you to wrap your brain around at this stage, but that is a good, not bad, thing for the situation you find yourself in. You are welcome to keep reading traditional notation while trying to play any classical repertoire (which i encourage you to do!) But, it is not only a waste of time while learning non-classical genres, it is actually a hindrance because it furthers the incorrect notion that what you play in detail should in some way already be decided for you by someone else.
It is very much a 180º turn mentally for a lot folks who have always considered black dots on white paper to BE music, as opposed to just be a recording of music. It sadly is what causes the “Oh, but I didn’t bring my music …” situation that arises so often when folks want to hear someone play. In addition, it keeps you from learning the most important music theory you need to play in these styles–reading chord symbols. So no, we stick to the musically “correct” style of notation for what it is we are learning and playing, that being lead sheets.
“Is my classical training and your method mutually exclusive, or are they complimentary?”
They are absolutely complementary! That’s the great news! Your previous experience at the piano will put you in good stead in multiple ways such as already being completely comfortable reading a one-note-at-a-time line in only the treble clef, and the finger dexterity and familiarity that comes naturally from the number of hours throughout your life that you have already sat behind a piano keyboard. On the flip side, the theory understanding you will acquire from learning to play chord progressions from chord symbols (as opposed to seeing everything notated) will give you unprecedented insight into your classical pieces once you go back and play them and start realizing you are playing many of the same chord progressions. It’s truly eye opening in a holistic sort of way.
“I completed the free intro lesson pretty easily. Should I begin at the beginning or start with a later course?”
I think I would suggest you start with Course 2 (or 3.) I absolutely think you should skip Course 1. In Course 2 you will possibly already know a lot of the “basic music” stuff I discuss (like some roadmap things like repeat signs, and some beginning notation stuff for true beginners) but in spite of that you will also get a LOT of eye opening “brain explosion” stuff for folks like you who have studied classical piano previously. I think it is well worth going over some things you may already know, to hear some of the more seminal “big picture” things such as–DO NOT try to read the lead sheet verbatim as it is intended to be interpreted as you see fit, or things like “play it the way it sounds best to you, not necessarily the way it is written.” I know it probably sounds like sacrilege to you at this point, but we are learning something far away from traditional classical piano and it takes a mental shift to separate the rules of classical from non-classical piano.
If you really wanted to start further ahead you could start with Course 3, although I will be mentioning things in the lessons I had referred to earlier now and then (that may be a bit confusing.) You can take a look here to see in-depth what is covered in every Course: www.pianoinaflash.com/syllabus
I hope that helps in your thought process.