There are several ways to do this:
1. Classical radio stations like to poll their listeners and come up with a "top 100," which means 100 most popular. Typically these lists have many pieces like "Pachelbel Canon" that classical music snobs (like me) don't consider to be "must haves."
2. Snobs compile lists of what we claim are the "highest quality," even if these lists don't have all of the best-sellers.
3. Pinhedz go even farther, and list things like Henry Purcell's Fantasias for viols, which make the list only because the pinhed personally likes them.
Another feature of this kind of list is that they are typically 100 or more if the compiler really includes everything considered to be in the "must-have" category, because there are about 100 composers in the top-notch category, each of whom produced several masterpieces. That would require several shopping trips, so I'll list something more scaled-down.
This is a mixture of radio station "top 100" selections, along with some snob/pinhed selections (which I'll put in bold type, because they're really the best):
I don't know if you like baroque, but here's some:
[Purcell -- Fantasias for viols]Bach -- Brandenburg Concerti
Handel -- Water Music
[12 concerti grossi]Vivaldi -- the 4 seasons
Classical:
Beethoven -- Symphonies #3, #5, and #9
[quartet op. 131 with Grosse Fuge), piano sonata op. #110]Berlioz -- Symphonie Fantastique
[Harold in Italy]Brahms -- Symphony #1
[Sonata for violin and piano #1, op. 78]Dvorak -- New World symphony
["Cypresses]Liszt Hungarian -- Rhapsodies #1 and #2
Mozart -- Symphonies #39, #40, and #41
Rossini -- Overtures
Tchaikovsky -- Capriccio Italiene, violin concerto and symphonies #4, #5, and #6
[Piano Trio op. 50]Rimsky-Korsakov -- Sheherazade and Capriccio Espagnole
20th century:
Bartok -- Concerto for Orchestra, violin concerto
[viola concerto and piano concerto #3][Ernst Bloch -- quintet and Schelomo]Georges Enescu -- Rumanian Rhapsody #1
[Sonata for violin and piano in the popular Rumanian style]Gershwin -- centennial collection (2 CD set--really great)
Khatchaturian -- Gayane Suite
[piano concerto]Mahler -- "Resurrection" Symphony
Prokofiev -- Classical symphonie and Suite from "Love for 3 Oranges"
[violin concerto #1]
[Schoenberg -- Verklarte Nacht] Shostakovich -- Symphony #5
[Skriabin -- late piano works (op. 65 through op. 74)] Richard Strauss -- So Sprach Zarathustra, Ein Heldenlieben,
[Metamorphosen and 4 last songs]Stravinsky -- The Firebird, The Rite of Spring
[Petroushka--complete if you can find it]I don't know if you like opera (I know I don't) but these 3 are essential (people who like opera would recommend Verdi and Wagner):
Beethoven -- Fidelio
Moussorgsky -- Boris Godunov
Gershwin -- Porgy and Bess
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I don't do it for the money, babe. I do it to entertain people.-- Susan Boyle