looking for ideas on must have classical music

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!

This link may be of interest to you.
https://www.nytimes.com/2019/04/19/arts/music/classical-music-piano.html?smid=nytcore-ios-share

@ott, "Classical music consists in a vast array of sub-genres, and almost limitless modes of expression."

Yes that's easily forgotten when you want a similar Classical thrill to some hard rock or harmonic pop.

Speed/ tempo is probably the main criteria I use to categorise music. I don't really enjoy too much of a mix match when it comes to tempo because that doesn't help to create a particular mood. At least not for me.