Come on! You can do it! Here's the bottom line: classical "aficionados" claim that this music is "not for beginners" because it's really not for THEM. Who are they to tell you what you may or may not like? So here's the list: 10 Essential Atonal/12Tone Works for Beginners:

Schoenberg: Five Pieces for Orchestra
Schoenberg: A Survivor from Warsaw
Berg: Wozzeck
Berg: Three Pieces for Orchestra
Webern: Six Pieces for Orchestra
Webern: Five Pieces for Orchestra
Webern: Six Bagatelles for String Quartet
Stravinsky: Agon
Penderecki: Threnody for the Victims of Hiroshima
Ligeti: Lux Aeterna