For all of his notoriety I have never found Cage terribly interesting.
He is certainly not representative of any group of composers of which I'm
aware--he was not the first nor the last to indulge in circus tricks and
call it music.  The works that helped me cross over boundaries and find
music in what I once called noise were Schoenberg's "Variations for
Orchestra" (go for R.  Craft's recording, avoid Karajan's) and Penderecki's
St. Luke Passion (which struck me as very powerful at the time and now
bores me silly).

No list of worthwhile 20th-century music (even that which I know) could
ever be complete.  Ives, Webern, Lutoslawski--just three that come to mind.
Like Schoenberg they have all written more-or-less traditional early works
(Ives' Symphony #1, Webern's Passacaglia and Im Sommerwind, Lutoslawski's
Concerto for Orchestra) as well as avant-garde stuff that retains its power
(like much of the work of that most shocking of all composers, Beethoven)
many years later.

I would not hesitate to recommend my own recordings that are available on
VMM CD's--you can check out my web page for some information and audio
examples thereof.

Aaron J. Rabushka
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http://www.cowtown.net/users/arabushk/