As such, I haven't learned piano from traditional lessons. I have been self-teaching piano since five years, but I've taken a few lessons since a few months. My current teacher reckons that I've actually taught myself an unusual amount, but have certain atypical strengths and weaknesses.
You may want to take a look at what I posted in the following thread: http://forum.pianoworld.com/ubbthre...to-a-new-adult-beginner.html#Post3010526
I'm a guitarist with a BA degree, and some piano courses were required. So I've already learned music theory, music reading and basic piano. I have no problem playing pop piano comping as long as it's not too challenging. I always regret not learning piano when I was a child (I took lessons for about one year). I asked a few friends who have been learning piano since they were young about what did they study.
In some ways, I find that our experiences may be similar. I can arrange most pop songs pretty quickly, within 15 minutes or so. I have basically done the equivalent of first semester harmony which I learned from an online course on Coursera, as well as just generally making a note of the theory behind the compositions I played. While I do not play the guitar, I learned piano largely by arranging songs I knew, or learning other people's arrangements. I would play any song that I could think of, or that a friend would request, as quickly as possible. Then, I would try and make use of several arranging techniques, some of which were quite difficult. I learned 3-4 classical pieces in the meanwhile, but must have improvised for hundreds of hours, and come up with rudimentary arrangements of hundreds of songs, which I would then improvise over. That lead to developing a facility with techniques such as octaves and fast arpeggios in various configurations, honestly quite beyond what a grade 8 student would be expected to play. Now that I'm learning classical piano, I basically started out at a pretty high level in a number of respects.
Regarding method books -- most of the teachers I respect online do not quite follow method books. They are useful inasmuch as they can be used to narrow down on weaknesses and provide some sort of structure to one's learning. I think what is probably more important is to play a number of pieces, maybe learning one every week or two, and trying to get as good as you can with those. I believe that plain old exercises are less useful for adults, as opposed to simply playing a number of pieces and getting used to the techniques in context. I have found scales and arpeggios to be useful, and knowledge of how to move the hand efficiently. As an adult, you're probably not as good as a child at mimicking other people's movements. So it's a good idea to also be aware at an intellectual level about efficient hand motions and how they work. Check out Graham Fitch, Josh Wright, and cedarvillemusic on Youtube if you haven't already. You should aim to be acutely aware of tension in the hand. Method books as such aren't useful beyond achieving a basic understanding of technique, since so much involves really subtle hand movements, which are difficult to communicate and can easily be misinterpreted over text. More than doing the exercises, imo, it is important to note how you're doing them. Your hands should feel really light, and the motions should feel effortless. It doesn't matter whether or not you do exercises if you achieve those ends through other means, such as by playing a wide range of repertoire.
Actively listen (and by this I mean really listen to the minutiae) to a LOT of classical music, maybe about an hour a day at the starting. Hopefully, you do enjoy listening to classical music, since you're attempting to learn it. You want to gain an instinctive understanding of the idiom as far as possible. Listen to pieces multiple times and try to understand what really makes them special. Listen to the great concert pianists, make a note of their differences, find out what things you like, whether there is someone who really appeals to you, etc. Eventually, you will gain a better instinctive picture of the landscape.
It is possible to achieve a pretty decent level on your own, so don't necessarily worry about that. It helps if you have time on your hands. In the first few months, I was playing the piano/keyboard for several hours a day, obsessively trying to play pieces I enjoyed (while driving my roommates mad!). It paid off; however, if you have a really hectic job or something where you only have half an hour each day to spend, it might be a good idea to get a teacher, because you can then offload all of the planning onto them in some sense. In that case, make sure to get the very best one you can and be really picky, because a bad teacher is worse than no teacher. If you have high aspirations such as wanting to play Chopin etudes at a high level, regardless of how talented you are, I think it's a good idea to get a teacher on balance. I have yet to come across a self-taught student who managed to play them well.