Suggestions, please...

Please list the particular pieces of compositions that you like from your list of composers.

Rachmaninoff not classical??
If he lived in 20th century id doesn't mean that he's not classical. He is by all his means and ways to write music and so is Prokofiev, Skryabin...
Alphred Schnittke is another story...

Auaarons:
Mozart-everything.

Vivaldi-"The Four Seasons" and "Gloria"

Saint-Saens-"The Swan" and "Danse Macabre"

Rachmaninoff-Piano Conc. 2, Piano Conc. 3, Variations on a Theme from Paganini

Gershwin-everything, but "Rhapsody in Blue" is my favorite.

Slipknot1-Ancient Airs and Dances sounds interesting...I will have to check that out. I've heard of the "Goldberg Variations" but don't know if I actually know them.

Marakanetz-I said that because I had a piano teacher who constantly corrected my for saying he was "classical."

Thank you everyone!

The piano teacher was technically correct. "Classical music" is music of the classical era while Rachmaninov was of the "romantic" era. We tend to use the term "classical" to cover several eras.

You could ease into baroque with concertos by Handel, Vivaldi, Bach and Albinoni. Analekta has a good disc of Vivaldi string concertos with Angèle Dubeau and her Stradivarius. They also have a killer Handel recording with Karina Gauvin, listen to a snatch here:

UHF magazine's Analekta page

You might also like Purcell, the more joyous things with brass to start with (Odes and Welcome Songs), and Haydn, the cello concertos maybe. There are millions of recordings of these, my favourite being the one with Iona Brown conducting and Truls Mork on the cello (Virgin).

I also think solo piano is a good way to get to know a composer. Listening to pieces from different periods, from Bach to Keith Jarrett, you get a feel for how different times led composers to work with the same limits in different ways. It's amazing how contemporary a Haydn piano sonata can sound.

Oh, and don't forget the late Schubert trios.