The piano is a beautiful instrument both to look at and listen to. When someone decides to take lessons on the piano, they don't know what it is they are looking for in style, technique, or teachers. And sometimes they wonder if they should learn on their own, or get a teacher. This article will hopefully help you in your decisions. I'll add more information over time.
I find two common problems in deciding to teach yourself piano. First, if you have a question there is no one there to answer it for you, and you usually end up doing something wrong with no one there to correct it. In the end, it is harder to break bad technique then to do it right the first time. Second, creative people have a tendency to not stay focused. If we have someone there to 'make' us do what it is we wanted to do in the first place then we stay on task. We really do need that help to stay focused. I say this from my own experience, both as a creative person and as a teacher of creative people. So, if we have a teacher we tend to stay more focused.
Two of the most important studies at the piano are fingering and counting. Without correct fingering, your playing will sound choppy. Without counting the song will be unrecognizable, and you will not be able to play with a singer or band. Not all piano teachers insist on fingering or counting. If yours does not, ask him/her to insist on correct fingering and counting.