I think it is good to find a genre within classical and explore that for a while maybe?
The actual word "classical" encompasses such a vast area.
I'm very keen on impressionists such as Debussy, Ravel and others. In fact I'm a huge fan of Maurice Ravel's compositions. But I also spend a lot of time listening to the nationalists such as Bartok. At present I'm exploring the works of George Enescu, who is somewhat expressionist and somewhat nationalist :)
Personally I don't tend to recommend "flagship" works to people who are getting into classical such as those massive well known symphonies such as those by, say, Beethoven. They are absolutely fabulous of course, I love them and have them, but I think their very flagship-ness makes it hard to get your head around them at first.
There are lots of differing opinions in classical music of course. I notice someone mentioned Furtwangler the conductor. I confess I am not one for Furtwangler at all, I find his performances of Beethoven and Mahler symphonies to be very uninteresting personally, however that is in no way to suggest that the other person's view is not valid, it is just my way of seeing things!
There are many superb works listed already in the thread. I did see this:
Bartok - Conerto For Orchestra & Music For Strings, Celesta & Percussion as performed by Seiji Ozawa & the Saito kinen orchestra on Philips
I love the Concerto for Orchestra by Bartok and that is a superb version. Another piece by Bartok is the Miraculous Mandarin Suite. Bartok of course is 20th century and I think you might find it is easy to strike up a relationship with his work.
The Miraculous Mandarin Suite starts with an impressionist sequence of a busy street. There is so much in that short "scene", so much about modern life. You might find the work quite captivating.