One of the difficulties about learning to play a new instrument is figuring out a repertoire of easy yet great sounding pieces. Here is a suggested list of nine pieces that fulfill this perfectly.
One of the important parts of a repertoire for the classical guitarist is understanding that the music of the classical guitar spans several hundred years and several genres of musical history. This repertoire gives you a nice cross section of these times and genres without being too difficult to play. It is a great selection that shows off the incredible range of expression found in the classical guitar.
Moonlight Sonata - Beethoven - If you are a real beginner and would like to play an easy song that sounds great this is the first piece you should consider. It sounds absolutely beautiful in a haunting kind of way and it is a nice slow piece so you will be able to master it with little trouble. This is a great first classical guitar piece. It is a good example of the Romantic period of classical music as expressed by the guitar.
Allegro by Mozart - Another very easy piece to play and it sounds great. It has more of an early classical music feel to it. You will have heard this piece before and it won't take you long to learn this. This is a great example of early classical music.
Pachelbel Canon in D This is a gorgeous piece for beginners. It is very famous and sounds wonderful. It has a beautiful harmony and melody. If you are looking for a piece of sheet music thats not too hard to play and sounds perfect for the classical guitar.
Claire De Lune Here is another great piece for the beginning classical guitarist. The best way to describe this is "Pretty". It is just a pretty piece and no doubt you have heard it before.
Fur Elise - Beethoven - Awesome sounding piece, this is one of my favorites and if you are new to classical guitar or classical music I guarantee you that this piece will be familiar to you - It is almost as famous as Beethoven's fifth.
Prelude in E Minor by Matteo Carcassi - Very easy piece to learn and sounds great because of the minor key. Great first or second piece to learn and right out of the Carcassi Method for classical guitar.
Espanoletta by Gaspar Sanz - Very easy piece to learn and it sounds great. It has this great feeling of being Spanish and also being from the early classical period. It is quite unique and kind of sounds like something Mozart would have written while on vacation in Spain!
Adelita by Francisco Tarrega - Awesome piece and one of my favorites. This is the first piece I had mastered for my repertoire. It is very Spanish in a slow and non-flamenco way.
Spanish romance - great sounding piece and a staple of every classical guitarist. It has a great melody and is played slowly so it sounds great without being too hard to learn.
All of these pieces are staples of the classical guitarist and the sheet music for them can be found at music stores or online. With a little digging you can probably find free transcriptions.