Peggy Lucero is contemplating the following "starting" list for a classical
collection:

Adams: Harmonielehre
Barber: Medea's Meditation and Dance of Vengeance
Bartok: Music for Strings, Percussion and Celesta;  Miraculous Mandarin Suite
Berg: Violin Concerto
Corigliano: Symphony no. 1
Hindemith: Mathis der Maler Symphony
Ives: Symphony # 2;  The Unanswered Question
Janacek: Taras Bulba
Mahler: Symphony #9
Prokofiev: Scythian Suite
Ravel: La Valse
Schoenberg: Gurrelieder
Shostakovich: Symphony # 1
R. Strauss  Also sprach Zarathustra  (Thus Spoke Zarathustra)
Stravinsky: The rite of Spring
Webern: Passacaglia, opus 1

My reaction is OUCH.  Fine, if you are well versed in classical music, and
into the twentieth century...  But even there I would hardly have included
Corigliano or Barber ...

Some specific changes I would recommend:

Bartok: either the 3rd piano concerto, since she likes piano and this is
a very approachable piece which combines much of the best of Bartok, or,
despite the dislike of Opera, Bluebeard's Castle - fabulous music in a
short operatic form.  Personally my favourite piece is the Solo Violin
Sonata but I know that is a bit acerbic for some people ...

Mahler: Symphony 9 is fabulous but a dreaded tough nut to crack without
an extremely solid traditional harmonic background.  (Bitter-sweet does
not work if you do not see what he is doing with diminished 9ths).  I would
have thought Mahler 5 or 6 (even 1 or 2 to start with) before going to the
ineffability of 9!

Prokoviev: I would have thought the more approachable ballet music (Romeo
and Juliet, Cinderella) would have been better to kick off with.  But if
you like piano music, try the "Sarcasms" before the big sonatas!

Ravel: I do not think La Valse is his best work.  I would recommend the
piano concerto instead - hints of the classicism that underpinned so much
of Ravel and, let's face, some gorgeous tunes as well as jazz ...

Schoenberg: why not start with end of an era, Verklaerte Nacht, before
hitting Gurrelieder and/or going to something tougher like the Chamber
Symphony?

Strauss: I would have thought Don Juan or Till Eulenspiegel or the Suite
from Rosenkavalier rather than Also Sprach; more representative of Strauss
and IMHO better works.

Stravinsky: Rite is of course seminal; but if Peggy is a newbie, would it
not be better to start with Firebird, and move to Rite later? Rite is its
own vocabulary, miles apart from what went before or even after ...

I would also have included music by Debussy (probably La Mer), Tippett
(Ritual Fire Dances), de Falla (Three cornered Hat) and Britten (Sea
Interludes from Peter Grimes).

But the great failing of this list is that it pre-supposes a classical
vocabulary.  So let's hope Mozart, Beethoven, Brahms etc figure in the
background too!

CR