New to classical music

For eclectic I would also suggest Arvo Part.

@elizabeth , two really great recommendations; Beethoven
and Rachmaninoff piano concerti.
 But I have to strongly disagree with your opinion of Mahler. I would say that it's not for beginners.

Here are some of my favorites that a listener who appreciates the eclectic might appreciate:

Alan Hovhaness - Symphony #50 "Mount St. Helens"
"And God Created Great Whales" Opus 229

Olivier Messiaen - "Des Canyons aux Étoile"
"Turangilila Symphony"

Bejamin Britten - "Prince of the Pagoda"

Colin McPhee - "O Bali"

Igor Stravinsky - "The Rite of Spring"
"Petrushka"
"The Firebird"

Bela Bartok - "Concerto for Orchestra"
"Music for Strings, Percussion, and Celesta"

Hector Berlioz - "Symphony Fantastique"

Einhojuhani Rautavaara -"Cantus Articus "Concerto for Birds and Orchestra."

All of these works showcase the power of the orchestra in different ways.

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