In reply to The Lemming:
J.S. Bach is clearly the GOAT, but some of his music needs concentration and a little knowledge to fully enjoy (e.g., the Art of Fugue or the Mass in b minor).
Anyway, I can thoroughly recommend exploring classical music on youtube, the diversity of recordings on offer is fantastic. Quality may vary, of course, and don´t read the comments if you want to keep your sanity.
I often use it to compare various recordings of the same piece before buying (I still prefer my CD player over any compressed streaming format).
To give you a quick list covering some main periods:
I would start with some choir works by Monteverdi and Schütz, ,
then a bit of Purcell (e.g. excerpts form Dido and Aeneas),
loads of Bach (the allofbach website of the Netherlands Bach society is fantastic, listen to the completely overplayed Toccata and Fugue BWV 538 over your head phones, the aoB version is simply at another level of performance! They also have a great selection of vocal works),
Mozart mainly for his operas and symphonies,
Beethoven for his symphonies and chamber music,
Mendelsohn (symphonies and vc)
Schubert (songs and chamber music),
Brahms, Rachmanninov (symphonies again),
Sibelius (mainly the violin concerto),
Bruch (Kol Nidrei and again the violin concerto),
Shostakovich (symphonies and Jazz suites)
Gorecki (Symphony of Sorrowful songs)
Gershwin (Rhapsody in Blue)
If you listen to any of these on youtube chances are you will find lots of related stuff that you may like as well.
I like to think that I have a rather broad knowledge of classical music, but still regularly find fantastic stuff I had never before even heard about!
CB