Although these works are not necessarily written by lesser known composers, here's a list of pieces you should listen to along with suggested artists:
Brahms- Symphony No. 3 (all of his stuff is great though) with the CHICAGO SYMPHONY
Beethoven- Symphony No. 7
Vivaldi- The Four Seasons
Mendelssohn- Violin Concerto Op. 64 in E minor (with SARAH CHANG or HILARY HAHN)
Elgar- Cello Concerto Op. 85 in E minor (featured in August Rush) with JACQUELINE DU PRE
I could list others, but I'll stop there... well almost. I am a singer, so let's not forget vocal music (I feel opera is under-appreciated)!!!!!!
Listen to Renee Fleming (soprano). You'll either love or hate her, but I love her CLASSICAL singing. Please don't listen to anything from her Dark Hope album...
I LOVE THE COMPOSER ROBERT SCHUMANN!!!!! So, listen to his Frauenliebe und leben with a mezzo-soprano (preferably Anne Sofie von Otter) singing it.
Finally, listen to Schubert's Erlkonig. I posted a female singer, but you should also listen to a male singing it. Look at the translation while you watch it.
Finally finally, if you want to delve into opera, the best way is to go to one or to at least watch a video of one. I suggest something by Puccini. Madame Butterfly was my first, but La Boheme (what Rent is based off of) is great also. If you want to watch a comic opera, watch Die Zauberflote (The Magic Flute) by Wolfgang Mozart.
I hope this helps! Let me know what you think of this music (and please quote my post or I may never know you replied).
P.S. Check my signature. Nodame Cantabile is an anime that can expose you to tons of new Classical music.