The point was to create a STARTER LIST, not a participatory "I like teh classical twoo" thread.
In that case, I'd lose Anton Bruckner. Lovely music, but it can be a bit difficult for people who are new to classical. You should at least hear Beethoven's symphonies before you listen to Bruckner so you get an understanding how symphonic structures work. Then again, anyone who can sit through Obscura will probably find Bruckner to be easy listening.
My reccomendations for people who are new to classical music:
1.
J. S. Bach: Brandenburg Concertos; Goldberg Variations; A Musical Offering
Some of his more sensual pieces. Calm and joyful music with substance.
2.
Ludwig van Beethoven: 3rd, 5th, 6th, 7th, 9th Symphonies
Obvious choice. Symphonies don't get better than this.
3.
Wolfgang Amadeus Mozart:: Requiem, Piano Concerto No. 20
The 20th Piano Concerto is surprisingly dark for Mozart and one of my favourites. The Requiem is one of his most popular pieces for a reason.
4.
Johannes Brahms: 4 Symphonies, 1st Piano Concerto, Horn Trio
His first piano concerto is magnificent. The first movement is one of the highlights of romantic music.
Don't ignore his chamber works. The symphonies are great but you miss out on a lot if you only listen to them.
5.
Franz Schubert: Die Winterreise, "Death and the Maiden" String Quartet No. 14
Beautiful romantic music. One of the best composers from that era, besides Brahms and Bruckner
More advanced listeners might want to try:
Johann Sebastian Bach: Die Kunst der Fuge
Probably the most complex piece of music ever written. It's still enjoyable if you know nothing about music theory, though (but it helps if you do). I believe this "theoretical" piece actually speaks more of Bach's spirituality than his sacred works.
Anton Bruckner: 8th Symphony
His greatest achievement. It took me a while until I understood it but my patience paid off. A thundering first movement, a scherzo that wouldn't seem out of place on a metal album, a beautiful adagio and a finale with marvelous, powerful themes. What is most admirable about this is his sense of perspective: The coda of the last movement features the main themes of all the four movements combined. That Bruckner was able to do things like this without descending into unlistenable chaos is genius.
Gustav Mahler: 6th Symphony
The instrumentation includes a huge wooden hammer. Need I say more about this?