Starting to listen to classical music - where to learn more ?

Spotify.. got into Chopin that way.

Search youtube for Leonard Bernstein's Young Persons Concerts. Joshua Bell did a few as well but haven't seen them.

After that, Classic FM does some really good stuff and you can access on Tunein.com. Live that station.

If you are near the Nat Concert Hall go to the Friday concerts now and again.

Where possible, listen to full works.

Now for some recommendations:

Piano:
Anything by Chopin. Both Lang Lang and Yevgeny Kissin have comprehensive Chopin albums. Journal Intime by Alexandre Tharaud also worth a go.

Beethoven Sonatas: check out Daniel Barenboim or Wilhelm Kempff here

Anything by Liszt

Rachmaninov preludes

Piano plus orchestra:
Rachmaninov Piano Concerto 2 plus Rhapsody on a Theme of Paganini
Beethoven Piano Concerto 5
Saint Saens Piano Concert 2 or 5
Brahms Piano Concerto 1 or 2
Mozart Jeunehomme concerto
Also the John Field and Charles Adams concertos are worth a listen. Bach fir 4 pianos also fun.

Violin plus orchestra:
Concertos by Beethoven, Sibelius, Schuman and Tchaikovsky. Anything by Vivaldi

Random orchestra
Carnival of the Animals by Saint Saens
Finlandia by Sibelius
Peer Gynt by Grieg
Appalachian Spring by Aaron Copeland

Great to see another classical listener on here. This is a post i made on TalkClassical a while back.

I began listening to "Classical" about 2 years ago. Im going to give a very simple breakdown from my relatively limited but enthusiastic experience so far (so I'm leaving out pre-baroque and most 20th century for example).

As a beginner I found that there were a number of different sounds. Broadly (though there can be crossover sometimes but to keep it simple)
Orchestral
Chamber music
Solo music
Vocal
Opera

and a number of periods, roughly (I've picked 3 composers i like for each)
Baroque (Bach, Handel, Vivaldi)
Classical (Haydn, Mozart, early Beethoven)
Romantic (Late Beethoven, Schubert, Brahms)
Modern (Stravinsky, Debussy, Ravel)

This is very individual but i would try a few of the following on Spotify/You Tube to get a feel for what you like. One important lesson when i started, i had to listen in a different way from my old rock/pop method. I tried to listen for at least 30 minutes without ever skipping (generally listened to the whole piece in one go). It also took me a few listens of some pieces before they really started to get into my brain. However once they got in they were in deeper than almost anything id ever listened to before.

Here are 6 which give a decent sample (I've not include any vocal works yet)
Bach - Well tempered clavier - solo piano
Mozart - Piano concerto no 21 - Orchestral
Schubert - Trout Quintet - Chamber music
Beethoven - 5th Symphony - Powerful and possibly familiar orchestral
Debussy - Suite bergamasque (particularly Clair de lune) - Solo piano
Stravinsky - Rite of Spring. I don't know exactly how to describe it, leave it till last, it will sound different!

This should give you a decent start, i began with a few pieces and got familiar with them. I found i liked some composers a little more than others and then used this site and a few top 50 recordings lists to go deeper.

Please let us know how you get on.