WilliamMc, welcome to the fun. Enjoy the ride and good luck!
Here's a couple of links that I found incredibly useful for self-teaching:Dr. John Mortensen
A piano professor from the Cedarville University, everyone who wants to self-teach (well, anyone who starts piano really) should check out this video series first. He explains some of the basics of piano technique which are great to understand how to play in a relaxed, healthy way. Josh Wright
This guy has a number of excellent free videos with tips and tricks on technique and how to practice. He uses advanced pieces to demonstrate his stuff, but his advise is great for all levels. Bernard posts index 1 Index 2
Ten years ago there was a teacher called Bernhard who was very active on the PianoStreet forums. He wrote about everything, his way of teaching, how to practice, about self-learning, about good pieces to play etc.
His posts were (and are) highly regarded by many, so much that some people actually created an index to his posts. Great food for thought about the way you approach learning and playing the piano. Even if you don't agree with everything he wrote, it is very helpful to at least think about it.
The two links above provide an indexed overview of his posts, no need to search yourself. Fundamental Keys
If you are interested in classical music (like me), I highly recommend you work on the Fundamental Keys method book in addition to Alfred's 1. It is the best beginners book for classical music according to many forum members, contains all original scores (so no watered down arrangements) and is probably the best investment you can make (I think it costs $15 or so).
Be sure to get the original version though. There's a new version out, which was supposed to become a 3 part series, but it looks like the author stopped working on it after part 1.
Hope to be of some help.