Classical can be one fo the trickiest areas for MP3's and other music files. Almost everyone udnerstands the laws about intellectual property for modern era music. At the most basic, free music from anywhere other than the band itself is illegal. Classical gets complicated, because some of is clealy in the public domain, some rights belong to the orchestra that recorded and released the music and some rights could belong to owners of the estate or music catalog of more recent composers. I make no claim to understand the complex fine points of the law. I have always figured on the "maximum crap" rule, which simply states that you should assume the most restrictive law and worst legal penalty you can think of will apply. (Harsh and negative, yes, but it keeps me out of trouble.)
As for your interest in classical music, GREAT! Besides the old standards, such as Bach, Mozart and Beethoven, I'm a Wagner fan. He gets a bad rap because of the association with Nazi regime, but for really powerful stuff, Wagner was one of the best. Had he lived today, he would be a Hollywood theme song composer, no doubt.
After that, don't overlook what some modern composers have done, outside the mainstream. Many modern "classical" composers are very experimental with in the framework of a symphony orchestra. Part of my interest here is personal; I have a cousin who writes orchestral pieces. He did a very moving commemorative work for my younger brother after he passed away.