Here's a list of very famous classical works composed between 1650 and 1950 which might help you build your own ''Basic Classical Music Library'' (including 10 'really basic' works identified with an *).
-----Baroque era (c. 1600-1750)-----
* Vivaldi: ''The Four Seasons'', Violin Concertos Op. 8 Nos 1 to 4
* Bach: 6 Brandenburg Concertos BWV 1046-1051
- Bach: 4 Orchestral Suites, BWV 1066-1069
- Bach: Toccata and Fugue in D minor for organ, BWV 565
- Handel: Water Music
- Handel: Music for the Royal Fireworks
- Handel: Messiah (in particular the ''Hallelujah'' chorus)
-----Classical era (c. 1750-1800)-----
* Mozart: ''Eine kleine Nachtmusik'', Serenade No. 13 for strings in G major, K. 525
- Mozart: Symphony No. 40 in G minor, K. 550
- Mozart: Requiem in D minor, K.626
* Haydn: Symphony No. 94 in G major ''The Surprise''
- Beethoven: Piano Sonata No. 14 in C-sharp minor, Op. 27 No. 2 ''Moonlight Sonata''
* Beethoven: Symphony No. 5 in C minor, Op.67
- Beethoven: Symphony No. 9 in D minor, Op. 125 ''Choral'' (4th movement with ''Ode to Joy'')
-----Romantic era (c. 1800-1900)-----
- Rossini: Overtures (William Tell, The Barber of Seville)
* Schubert: Symphony No. 8 in B minor, D.759 ''Unfinished Symphony''
- Berlioz: Symphonie fantastique
- Mendelssohn: Symphony No. 4 in A major, Op. 90 ''Italian''
* Chopin: Various piano works (Polonaise No. 6 in A-flat major, Op. 53 + Étude in C minor, Op. 10 No. 12 ''Revolutionary + Nocturne No.2 in E-flat major, Op. 9 No. 2, etc.)
- Liszt: Various piano works (Hungarian Rhapsody No. 2 + Liebestraum No. 3 + Sonata in B minor, etc.)
- Wagner: ''Ride of the Valkyries'' from Die Walküre (+Various orchestral works)
- J. Strauss II: An der schönen blauen Donau (''Blue Danube Waltz), Op. 314 + Various waltzes
- Brahms: 21 Hungarian Dances (orchestrated)
- Tchaikovsky: The Nutcracker, Suite Op 71a
* Tchaikovsky: Piano Concerto No. 1 in B-flat minor, Op. 23
- Dvorak: Symphony No. 9 in E minor, Op. 95 ''From the New World''
- Rimsky-Korsakov: Sheherazade Op. 35
- Mahler: Symphony No. 5
- Rachmaninoff: Piano Concerto No. 2 in C minor, Op. 18
- Debussy: Prélude à l'après-midi d'un faune
-----Since 1900-----
* Ravel: Boléro
- Stravinsky: The Rite of Spring
- Prokofiev: Piano Concerto No. 3 in C major, Op. 26
* Orff: Carmina Burana
- Gershwin: Rhapsody in Blue for piano and orchestra
- Shostakovich: Symphony No. 5 in D minor, Op. 47
- Barber: Adagio for Strings, adapt. of String Quartet No. 2, Op.11, 2nd mvt.
Best regards