Hey BP:
Congratulations on taking the first step towards your goal of being a musician. I will add a few thoughts to the other excellent advice offered here (I'm also a piano teacher, who earned a piano degree as an adult).
Focus on the advantages of being an adult student: desire to learn is often stronger, more disciplined in practice routines, better intellectual grasp of musicianship. These things will help make up for less flexibility in the muscles, tendency towards being overly critical on self, unrealistic expectations, greater nervousness in public playing, sometimes more erratic practice and lesson times due to work schedule, etc.
Have you thought about your goals: What type of musician do you want to be? (ie play public recitals, just goof around on your own, play in a band, even teach, etc.) Don[t be afraid to dream big! But realize that it will take patience and dedication to get to that place, and at this point you probably will not be able to have a career as a concert pianist (although, you just never know!). What style of music do you want to play? Each style has basics that need to be mastered.
BTW, each of the aforementioned activities are important for all around musicianship: playing in front of others (even if it is just your family and friends) develops the skill of polishing a piece and expressing it for others to appreciate. Playing with others: your teacher will probably play duets with you, that's always lots of fun, and playing with other instruments is something you will want to experience. It teaches a new set of skills: listening to others, being really careful with timing, creating something wonderful as a group. Experiment on your own--be creative, explore all your instrument has to offer, compose something original, then share it!
Enjoy the expressive elements of music: when learning a piece, always think: what story or message do I want to express with this? What was the composer's intention? Always take it to that next level--even Mary Had a Little lamb, for example. Get the mental picture of the story: bright, happy, a bit naive, etc. and reflect that in the style of your playing. When you are first learning, it is easy to get bogged down in the notes, but once you have this mastered, go to that next level of expressing something. That is when you are an artiste
Pay attention to chord structures. Identifying/Using chords in learning to play will add greater richness to your music, make it easier to memorize the music, help with improvising, etc. But also learn to read the actual notes. This will open up the whole world of written music rather than just falling into the trap of playing by ear.
Watch out for tension in the shoulders, arms, wrist and hands. Check frequently and stop and relax if it is happening. Pain is NEVER a good sign. Check often for proper curve of the fingers, that you are sitting correctly, etc. until these things become a habit. Break your practice session into segments. Look away from the music every 15 minutes or so and focus on something in the future (I wrecked my eyesight my too much intensity on my scores--had to get glasses ) Get up and walk around after 30 minutes. Identify the trouble spots in whatever you are playing. Practice these first. Don't waste time going through the entire piece over and over. If your fingers are stumbling in measure 6 and 7, then focus your work there. Practice smart!
I have a sign in my music studio for my students. This reflects my philosophy of music:
Countless,
unseen
detailsare often the only difference between
mediocre
and M
agnificent.Enjoy your musical adventure and keep us posted on your progress
PS. There is a myriad of information on the Internet you might want to look at once the basics are mastered. Pm me if you want at any time, I can refer you many excellent sites and books. What series is your teaching going to use to teach you?