Check out the work of Ferdinando Carulli. He composed a number of simple classical pieces designed for students. He wrote a method book 200 years ago that is still in print -- I have a copy and it is filled with useful, simple songs & exercises.
His "Adante" was one of the first pieces I learned on my acoustic -- you can find many amateurs playing this piece on Youtube.
You can also find free sheet music & tab of his work on the internet with a little digging.
this is the absolute best music site I've come around. It has everything you'll need to play classical guitar. Lots of people to help on the message board and they have essentially a list of pieces for you to learn from beginner to pro.
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