I'm no expert, but I would certainly suggest these excellent CDs:
I read The Rest Is Noise last year and really enjoyed it - however I agree it's a little difficult to throw yourself into it by going to the CD store and purchasing CDs. I also suggest Ligeti - Disc 2 of The Ligeti Project is simply sensational. I also really like this disc as well:
I'm a big "fan" of Mozart (I use quotes because it seems kind of preposterous when I say fan in the context of Mozart) and Berg and the pieces on this disc are fantastic.
I second the Messiaen as essential, and perhaps dipping into The Planets by Holst, although these suggestions may not be as contemporary as you'd like.
Also really important in my mind is the Shostakovitch Edition box set, the chamber symphonies and concertos are fantastic and the performances are exception. I was lucky enough to find it very cheap and I suggest downloading it because a) he's dead and b) I've seen it priced at $170 smackaroos.......
I'd also say that while they aren't contemporary pieces Goulds Goldberg Variations should stray far enough out of the realm to be considered.......
Oh and there's a great double disc set from Penderecki that's fantastic.