Where to start with piano

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my best friend has been playing for 10 years and is ridiculously good. I just started taking piano from and old choir director so that I can play while I sing. Because I'm a singer I already understand most of the theory and chords structures, etc. I've been told that the best place to start would be learning inversions and playing through chord progressions in differnent inversions. Do you agree with this, and if not where do you think I should start?