One of the most difficult things for a beginning classical guitarist is trying to find a repertoire that is not too hard to play but still sounds good and has a nice variety of pieces. Here is a nice list of guitar pieces that fits those requirements nicely.
You can probably browse around the web and find some free versions.
Range of Repertoire - these pieces span quite a few different centuries and genres. There are old pieces by Mozart and Bach, newer pieces my Beethoven and Tarrega and pieces from traditional classical guitar to Spanish guitar. Learning these pieces will give you a great standard repertoire that everyone can enjoy even if they don't listen to classical music because most of the pieces are very recognizable.
Classical Guitar Sheet Music - 9 Beginner Pieces
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.
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.
Pachelbel Canon in D This is a gorgeous piece for beginners. It is very famous and sounds wonderful. it just has a beautiful harmony and melody. If you are looking for a piece of sheet music that is not too hard to play and sounds perfect for the classical guitar this is a good one.
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 - quite unique and kind of sounds like something Mozart would have written while on vacation in Spain!. Good addition to a repertoire.
Adelita by Francisco Tarrega - Awesome piece and one of my favorites. This is the first piece I had mastered for my repertoire.
Spanish romance - great sounding piece and a staple of every classical guitarist.