I loved classical music in a cursory sense until I started studying it at UNT. Then I hated it because I was forced to listen to it constantly. So "learning to appreciate" classical music can definitely be a double-edged sword.
I would suggest going by what instruments you are most interested in. I myself am a classical guitar nut, so I love the work of Fernando Sor, Carcassi, Brouwer, and others.
An easy place to start with classical is to look into contemporary movie scores, most especially those by John Williams.
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