Dear m1469:
I think that's a good point: what is the fundamental repertoire? By the way, that's a question I'm concerned with as well in the last years. Here are some conclusions, that maybe can help. (Yeap: it's a huge amount of repertoire, but who's in a hurry? It would take about eight years to complete, I guess.)
Notice that although I believe in playing Bach, Chopin, Russians, I think that we can reduce a bit the number of pieces of those composers to include another ones. For instance, in Italy they play something as 20 or more preludes and fugues in three years (from 6th to 8th); there is a Master Degree in USA that requires 25 pieces by Chopin to the final audition. In spite the fact I think that both (and other ones) could be successful, I believe in a broader musical formation, and in a broader musical life.
Well, I'm almost off topic...

Here's the list:
Early Music: - some dances and one contrapuntal piece (fantasia, etc) by the english virginalists (Byrd in particular);
- a suite (or selections of it) by two contrasting 17th century composers, e.g., a german (Froberger) and a french (Jacquet de la Guerre);
- a contrapuntal piece (fugue) by Buxtehude;
- one piece by Frescobaldi;
- a piece by Telemann;
- a suite by Handel;
- Bach: a pair (or more) of inventions, a pair (or more) of sinfonias, a french suite, an english suite, at least four P&F (two of each volume). That's not usual, but a larger work (such as a toccata) would fit nicely;
- Scarlatti, D.: a pair of sonatas;
Classical Music:- Haydn: ten sonata movements, with at least two complete sets;
- Mozart: ten sonata movements, with at least two complete sets; one or two sets of variations; one large work (Adagio, Fantasia);
- Beethoven: 15 or more sonata movements, with at least three complete sets; some bagatelles; one set of variations;
- Schubert: two sonata movements; some small dances; one impromptu.
- at least one sonata movement and a character piece by one of the "lesser" composers: Clementi, Hummel, Czerny, etc.
Romantic Music:- Chopin: a mazurka, a valse, a nocturne, a polonaise, a pair of preludes, an etude;
- Schumann: a selection of one of his cycles (opus 12, for instance);
- Mendelssohn, Felix: a pair of Lieder ohne Worte;
- Liszt: a consolation, selections of his cycles (Anees, Harmonies), individual works (Nuages Gris, Bagatelle sans tonalite);
- Brahms: selections of his Klavierstucke; one rhapsody or a ballade (or both);
- some pieces by another composers, such as Field, Clara Schumann, Fanny Mendelssohn, Bennett, Thalberg, Rubinstein, Gottschalk, Alkan. Well, the list is endless, and probably Thalbergmad has better suggestions than mine;
Late 19th/Early 20th century Music:- Debussy: selections of (or eventually a complete) suite; a pair of preludes; one early work (Reverie);
- Ravel: Sonatine is the standard, probably because the rest (Miroirs, Gaspard, etc) is too difficult to think about;
- one or more pieces by other french composer: Faure, Honegger (I know he's not french), Milhaud, Poulenc, Satie, etc;
- Prokofiev: selections of his pieces; one sonata movement;
- Rachmaninoff: a pair of preludes;
- Scriabin: use your imagination...preludes, etudes, impromptus?
- Shostakovich: a pair of preludes; one prelude and fugue;
- Tchaikovsky: one piece of the Seasons;
- the russian repertoire of the period is huge, and important, and cool: Glazunov, Kabalevsky, Medtner, Mussorgsky, Stravinsky;
- Schoenberg's opus 19 is a must, but it's possible to consider something else (opus 11, 23 or 25);
- Hindemith: an interlude and fugue of his Ludus Tonalis;
- Bartok: selections of Mikrokosmos; other pieces (Sketches, Bagatelles, movements of the suites);
- at least a work by Janacek, Martinu, Smetana, Suk, or Szymanowky;
- Grieg: selections of his Lyrische Stucke;
- at least a work by Castelnuovo-Tedesco, Casella, Busoni, or Dallapiccola;
- at least a work by Albeniz, Granados, Falla, Turina, Mompou;
- at least a work by Cowell, or Barber, or MacDowell;
- at least a work by Villa Lobos, Camargo Guarnieri, Ginastera;
The
late 20th/early 21st century have so many choices, and so few standards, that it is probably a matter of taste, chance, and choice. Some ideas:
Berio's Encores
Boulez' Notations
Messiaen's Vingt Regards
Britten's Night Piece
Bennett's Studies
Stockhausen's Klavierstucke
Lachenmann's Ein Kinderspiel
Rautavaara's Preludes opus 7
Gubaidulina's Musical Toys
Cage's Sonatas and Interludes
Babbitt's Semi-simple Variations
Marlos Nobre's Ciclos Nordestinos
Me and my lists...anyway, hope it helps.
Best wishes!