I would recommend buying a beginning piano book, one for adults and a theory book... I would definitely always be working through theory as well as a practice book. A teacher is helpful, because in just 30 minutes they can point out so much that will improve your playing. And since your eager to set down and play (as many are
) a teacher will help point out things instantly that you may not pick up until much later on your own. I have a piano teacher that I saw for a couple of months and now just go to see every now and then when difficulties arise.
Plus, an experienced teacher always has extra information, they can answer all your questions and then some!