Thanks JLS! That would be a daunting thought indeed!
However, for people starting out, especially with rock and jazz backgrounds, like the original poster asked, which also mirrors journey into classical, here's what I would recommend - start listening in reverse chronological order.
Therefore, start with the modern/romantic era which may better appeal to your ears/sensibilities than the earlier classical/baroque era and work yourself backwards. Generally, ballet music is great fun to listen to as it has a storyline to capture your imagination too.
For example, here is a start (for a late night, can't sleep post)
Stravinsky's ballets (Gergiev's Rite of Spring, Chailly's Firebird),
Bartok's Concerto for Orchestra/music for strings, percussion (Reiner),
Mussorgsky's Picture's at an Exhibition (Reiner),
Ravel and Debussy Collections (Dutoit or Haitink), Also Daphnis and Chloe ballet music.
Dvorak's later symphonies (7, 8 and 9 - Kubelik, Kertesz, Szell Versions),
Mahler (my favourite is Haitink on Philips playing the 4th), and then work yourself into other symphonies/lieder.
Janacek String Quartets,
Prokofiev's Peter and the Wolf (many competing versions, great with kids),
Rodrigo's Concierto de Aranjuez (Pepe Romero or Julian Bream - jazz lovers will recognise Sketches of Spain or Jim Hall's Concierto).
Shostakovich symphonies/string quartets (especially symphonies 5 and 10 - massive historical significance rising against Stalin era),
Schumann's Kinderszenen (and you will know the origin of the Raymond's Complete man music - love the Moravec and Pires versions) as well as lots of piano music
Chopin - especially ballades (Persia) and nocturnes (Pires), but played by Rubinstein as well
Strauss - Zarathustra (well recognised dramatic beginning - Karajan)
Bizet - Carmen (de Los Angeles or Callas)
Liszt - Hugarian Rhapsodies (you may recognise from a Tom and Jerry cartoon - Cat Concerto)
Rachamninoff Piano Concerto 2 (to recommend a version is to start a debate - Ashkenazy perhaps).
Schubert - String Quartets (12, 13, 14 - I like the Belcea quartet a lot)
Tchaikovsky's Ballet Music.
Finally, a peep into the classical era - Beethoven's magnificent late piano sonatas (like my Solomon CD a lot, but many great artists).
I also have one by an obscure East German philharmonic. Not bad, but not great either. 
