If you are looking for some serious, important and impressive classical pieces for the guitar, then you should take a careful look at one of the most important guitar players that has ever existed, Andres Segovia. In a nutshell, he transcribed and revised songs by Bach, Weiss, Handel and Tarrega (all classical composers). His trademark songs are basically Chaconne, Gavotte I and II, and Prelude in D Minor. This songs are not easy, I personally have not learned them fully, but I can say this, they take time and patience to master. I hope this helps you out, if you need other classical pieces I can post them.