I just got into piano about a year ago, but didn't really take it as serious as I wanted to. Every single thread I see around are for people that haven't studied music at all, which isn't really the case for me. As back story goes. I've been playing flute for about 11 years now, been on bassoon for about 4, and have studied music theory for 2. I also did play keyboard for a semester in my highschools jazz band as well. I just don't know whether I should start diving into pieces that I want to play or if I should start going through piano exercises and all.
It sounds like you don't plan to take lessons. As a piano teacher, I may be biased, but I think you should. If you were intermediate/advanced and more or less knew what you were doing at the piano, I would recommend that you take a few lessons from a lot of different teachers before settling down with one for a while. Some teachers won't like that, but so much the worse for them. You can learn things of lasting value from even one lesson with the right person, in my experience. Before you dive into a piece, better check how deep the water is. You may want to play the piece, but does the piece want you to play it? There are so many pieces to choose from, it should be possible to find pieces that you enjoy that are not too hard for you. Of course I'm assuming that you want to play musically. Life is too short for exercises. You can get all the "exercise" you need from the pieces themselves, and it should be a lot more fun. (Playing an instrument is not exercise in the conventional sense anyway; you're training your nervous system.) But I do advocate being able to play all the scales, chords, arpeggios, etc. Your hand (your nervous system, really) has to become familiar with them; they're the "grammar", so to speak.
It means you was not interested at that time so this time you should start from the song you love most. It will help you get stick with the piano and inturn you will learn easily and most important thing you will enjoy the piano playing. You need to find out the notes of song you are interested in. So after passing this level you can go to the next level in short span of time as it improves your skills quite fast. So happy playing