looking for ideas on must have classical music

Excellent comments and suggestions above.

I would add:

Chrisropher Parkening, Parkening Plays Bach. Also John Williams’ recordings of the Bach Cello Suites. Another favorite guitarist is Carlos Barbosalima, any of his recordings.

Chopin’s Nocturnes and piano concertos, I like Pollini and Barenboim, but there are dozens of fine versions.

Schubert...some of his vast vocal music, I would begin with Songs for Male Chorus (Robert Shaw Chamber Singers), and sample some volumes from the Schubert Edition on Hyperion. I also recommend Schubert’s piano sonatas.

Mahler...the second symphony, Resurrection (again, lots of versions, but I usually reach for Gilbert Kaplan with the London Symphony). And explore some of his songs (“Lieder”), try Thomas Hampson or Dietrich Fischer-Dieskau as a start.

Brahms, his German Requiem and the Alto Rhapsody...Shaw and the Atlanta Symphony versions are nice. And some of my favorite, Brahms’ late piano music, say opus 116-119, especially the recordings of Stephen Bishop Kavacevich.

Some delightful fun, Gilbert and Sullivan, Pirates of Penzance or the Mikado.

Something ethereal, Bill Douglas’ Deep Peace, Ars Nova Singers

77jovian wrote (in part):

... Mahler...the second symphony, Resurrection (again, lots of versions, but *I usually reach for Gilbert Kaplan with the London Symphony*).

Good call. Kaplan is the ultimate amateur enthusiast. He recorded his version around 1986-7. He had fanatically studied the Resurrection notation for (I think) decades. He even owns Mahler's original Resurrection manuscript. Even as an amateur, Kaplan had so much credibility with the London Symphony that they followed his direction fastidiously.

Audio magazine's review (and they had many seasoned classical reviewers on the masthead) called the Kaplan recording "A Resurrection Symphony for the ages." Can't get much higher praise than that.

You'll like Presto Music. You can sample most of their music and much of it is available in one or another hi-def format. CDs are available for all. 

Classical music consists in a vast array of sub-genres, and almost limitless modes of expression. I like contemporary music. Composers (all Pulitzer Prize winners) you might consider: Meiczyslaw Weinberg, Joan Tower, Roxanna Panufnik, Lera Auerbach, and, if you're feeling a little outre, Missy Mazzoli. Schoenfield's Klezmer Rondos are delightful. The Bach oeuvre is vast and uniformly excellent, but I particularly like the cantatas - about 60 hours of music. Bartok is good to test your rig for speed and detail, and has a primitive, almost feral quality that can be deeply satisfying. 

That's my take. The journey is half the fun. 

A couple of suggestions for the OP and all the contributors to this thread: If you stream, check out the IDAGIO streaming service for Classical music exclusively.
Many search opportunities and wonderful suggestions for new recordings and even particular moods.
Also,  I invite all of you to check out the thread “Classical Music for Aficionados,”
Talk about Classical music.
Where have you all been?

The suggestions already offered are great. I would add: had a really wonderful experience learning about classical music, as well as it's historical precursors and variations, from a course offered by The Teaching Company, "How to Listen to And Understand Great Music," by Robert Greenberg. I had been a lifelong rock and jazz listener, and this series opened by eyes; it was a revelation. It's hard to appreciate the richness of classical music without an understanding of its form. The course is a wonderful and detailed introduction, also with lots of samples of varied genres. 
It's costly at its full price, but if you get on their email list they discount considerably and frequently. It's worth the wait.
Enjoy!