New to classical music

for piano - any well recorded, well performed Chopin.  

Baroque - Vivaldi and Bach

Classical - Beethoven (yes, he really was a genuine genius). Any Mozart (very tuneful and pleasant to hear)

Romantic - any of the Russian composers, specifically Tchaikovsky, Rimsky-Korsakov, Prokofiev, Stravinsky, Glazunov

Impressionism - Ravel and Debussy

Once your tastes mature, Shostakovich.  His symphonies #1, 4, 5, 6, 7, 8. 9, 10 and 11 especially.

If you want you can try Mahler and Bruckner but I just find it cold and sterile.  Just not what reaches my soul.  Go for Shostakovich if you want to experience a panoply of human emotions.

Good luck on your journey!

In referring to his eclectic tastes I’m not sure the OP was implying that he is looking for selections within the classical genre that might be considered to be eclectic, as opposed to works that are often referred to as "warhorses." Rather I suspect he was simply saying that his interests encompass diverse genres.

Under that assumption I would suggest the following works, that I believe to be particularly likely to be appealing to someone just beginning to become acquainted with classical music:

Dvorak, Symphony No. 9 (The "New World" Symphony)

Beethoven, Symphony No.. 6 (The "Pastorale," that was suggested earlier) and Symphony No. 7 (sometimes referred to as "the apotheosis of the dance")

Prokofiev, "Romeo and Juliet" excerpts

Prokofiev, "Classical Symphony," aka "Symphony No. 1"

Rachmaninoff, "Rhapsody on a Theme of Paganini" (for piano and orchestra)

Chopin, "Piano Sonata No. 3 in B Minor, Op. 58"

Schubert, "String Quintet in C Major, D. 956" (considered by many to be among the greatest pieces of chamber music ever written)

Brahms, "Symphony No. 1" and "Symphony No. 4"

Enjoy! Regards,
-- Al

Another is The Planets by Holst. Have to agree with Elizabeth, Brahms may put the op to sleep. Approach him after you have digested Beethoven and Mozart.

Surely Tchaikovsky Piano Concerto no. 1.  The other warhorses: Schumann and Grieg piano concertos.
Then some Wagner overtures and orchestral arrangements of excerpts.

Search for Denis Matsuev on Tidal. Pick a Tchaikovsky or Rachmaninoff, turn up the volume and enjoy