Contemporary composers. Please help.

Plenty of both living and dead composers. Among the living, try the following:

Krystztof Penderecki (try a choral work like "Credo")
Osvaldo Golijov (very accessible, and wide in range of types of music composed)
Eric Whitacre (young American composer of unique sounding songs).
Thomas Ades (I like just about everything he writes, even his opera)
Einojuhani Rautavaara (incredibly prolific composer)

Schoenberg wrote some pretty daunting serial works, but, he also composed a lot in a very melodic, late romantic style. Try Verklarte Nacht ("Transfigured Night") or his oratorio "Gurrelieder."

Bartok, Stravinsky, and Shostakovich are also good composers to listen to music with modern sensibility, but, music that still retains melody (while emphasizing new harmonic relationships). Benjamin Britten is one of the giants of the 20th century that should also be explored, along with Walton and Ralph Vaughan Williams.

Have fun in your explorations.

To elaborate on Bartok, to me, his string quartets are among the greatest works in that genre. Other 20th century string quartets to get are those of Shostakovich, the huge number of Villa Lobos quartets (some of the most overlooked works), and the quartets of Alwyn.

For choral works, there is a hybrid SACD/CD on the Chandos label, titled "Eternal Rest," that has terrific works by Mantyjarvi, Tichelli, Frank Martin, and Rene Clausen (all 20th century composers).

Brownsfan,

Not heresey to prefer the Britten string quartets more than the Bartok. Britten was quite the master of virtually all musical forms. I particularly like his chamber works, songs and his operas. Have you heard the Alwyn quartets? He is another overlooked English composer.

Lsd13,

You should get a listener's guide of some sort that describes the music, gives a brief biography and lists recommended recordings.

The hard part is finding the gems by composers who have little or no reputation who wrote only a few works worth tracking down. Given how personal favorites can be, it is hard to make recommendations for such composers or specific works (As an example, I like Rued Langgaard's "Antichrist," but it may not be a good general recommendation).

Lsd13,

Which Ligeti pieces have you acquired? He had quite a range of compositions and styles, from his early works which are reminescent of Bartok, to his electronic compositions and then to certain elements of the minimalist schools (he admire Reich and Riley).

I have a couple of additional suggestions. If you like solo piano music, look for the works composed for player piano by Conlon Nancarrow. These are unique works that are unplayable by a human.

From your list of likes, I would guess that you would like spare, contemplative works. You might find Ludovico Einaudi interesting, though it is a bit on the tuneful and "easy listening" side, and you appear to be much more adventurous. Still, worth checking out.