I started at age 40, from scratch, although I'd played classical guitar and viola as a student. I worked hard without a teacher and did not get all that far until I retired at 54. Then for 8 years I had a very good teacher, who took adult students seriously. By which I mean she didn't assume that all we wanted was to be able to struggle through the first movement of the Moonlight Sonata or Traumerei. She taught just as though we would one day want to apply to a conservatory. After those 8 years of working with a teacher and practicing 3 hours a day I was able to give a house concert playing the Bach French Suite in Eb, Beethoven sonata in E major Opus 14 #1, Chopin Nocturne in Bb minor Opus 9#1, Brahms Intermezzo in A and Romance in F from Opus 118, and the first movement of Janacek's In the Mist. Not dazzling virtuoso pieces, but interesting enough that it's definitely worth the work. Since then I played in some other local recitals and at churches, nothing much, but enough to get me to enjoy spreading the music around.
So my advice is be ambitious and don't be ambitious. Take yourself seriously and aim to play some serious, emotionally complex music, but don't be in too great a hurry. Figure out how to enjoy working on little technical problems, make small realistic goals. Also, make sure your teacher understands your goals and wants to help with them. Listen to lots and lots of music, not piano technical show pieces, but lots of orchestral, chamber, and vocal music from lots of different periods and composers. If you don't know much music theory, get a college level text and work through it, or find an online course. There are few things more absorbing than music - I go to bed at night looking forward to what I'll be able to practice in the morning. You'll have a great time.