For Schoenberg, I think the second string quartet is key, inviting you to breathe the air of other planets, as it moves emphatically towards serialism during the course of the work. The other work that comes to mind is the less well known Septet, op. 29, that I have always found to be quite an optimistic and cheerful piece.
For Berg, the
Lyrische Suite for string quartet is pre-eminent, and one of the most significant works of that time - there is much more colour and drama for me in this piece than in Schoenberg or Webern, frankly.
Moving forward, post WW2 the ideas behind serialism developed rapidly and significantly, from what was seen as a relatively narrow focus on pitch (ie, Schoenberg’s approach), towards an all encompassing theory covering every aspect of sound. Despite most of his work not being serial in nature, the key person, in my view, was Olivier Messiaen, as both a theorist and teacher, and also composer, and particularly his
Mode de valeurs et d'intensités (the second part of
Quatre Études de Rythme). This piece, along with Karel Goeyvaerts’
Sonata of Two Pianos, and Michel Fano’s
Sonata for two pianos, heavily influenced both Boulez in the writing of
Structures, and Stockhausen in the writing of
Kreuzspiel. All of these pieces, from the late 1940s and early 1950s, were hugely influential in defining the way in which post-WW2 music developed, along with the establishment of Le Domaine Musical by Boulez, where this strange music could meet an audience. Other highly significant pieces followed soon during the 1950s, including;
Boulez -
Le Marteau sans maître - to my ears, a sublime and unparalleled blend of austerity and eroticism, with a piquant dish of surrealism on the side.
Messiaen -
Catalogue d’Oiseaux - the surface descriptions of landscape and birdsong are underpinned by multiple layers which explore spiritual, transcendental and archetypal elements arising from Messiaen's experience - a
Golden Bough of contemporary music, if you will. (By the way, one of my main interests is the music of this period, and how both classical music and jazz then developed and interacted during the 1960s, and then what followed - the Catalogue is one of the most influential pieces, in my view - you can hear it in Cecil Taylor, Keith Jarrett and William Parker, and also Harrison Birtwistle and James Dillon, for example).
Stockhausen -
Gesang der Jünglinge, and
Kontakte.
Running in parallel, I'd also mention Elliott Carter's first string quartet of the early 1950s, which introduces ideas about how music can reflect both external (or real) time, and inner dream time. I think this work has some linkages to Berg's
Lyrische Suite, (which I need to do some more research on).
Paul Griffiths’ book
Modern Music and After describes very well many of the ways in which contemporary classical music subsequently developed, after the intensity of the 1950s. Alternatively, you could look at the discography of the Arditti Quartet, and especially the series of recordings on
Montaigne Naive, which move from the 2VS through to the present day. Discovering composers like Julio Estrada and Roger Reynolds through this series was a revelation for me.