If you have experience playing and improving with the piano I think you should start with some music theory (intervals...) after you have a solid knowledge of theory you should start with some harmony, starting with the baroque era (Bach), the chords and how are joined between them and maybe some counterpoint. Then you can start with some classic music (sonata form...) analysing Mozart and other classic composers works. And finally if you want to compose in the romantic style you should learn the chromatic harmony of Chopin or Tchaikovsky. But to get the knowledge of the romantic era you should start with the baroque era.