Actually I have zero knowledge, expertise or particular interest in that entire subgenre of orchestral music. I will check out some Youtube videos though. I am very boring and I play straightforward major-minor key bullshit. The more melodramatic and Jewish-sounding, the more I enjoy playing it.
I can't stand cookie cutter classical. There are a few tonal pieces that I do like though they are mostly Russian composers. Listen to Arnold Schoenberg's Verklärte Nacht. I consider it the most touching and beautiful piece ever written. It calls for a string septet. This piece was written shortly before Schoenberg developed his twelve tone system.
As for atonal and twelve tone, here are some excellent pieces that got me into the style of music:
Anton Webern, Op. 5 movement 1
George Crumb, Black Angels-Departure (This one is especially harsh)
Akira Nishimura, Threnody for Cello
Arnold Schoenberg, Variationen fur Orchester
Olivier Messiaen, Turangalila Symphony (The guy that I play music with and I base most of our writing on his modes of limited transposition)
Beware, all twelve tone and atonal is extremely unresolved. I found it uncomfortable to listen to when I was first exposed to it. It takes a few listens to adjust to.