Suggestions, please...

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.

...meaning Baroque being not classical either?

Marakanetz, is Baroque classical ? Some says yes, some says no, some says I'm off topic, some says I ain't ;o) Hope it helps old Fab4fan...

Checkout BBC on the web. It is one of the best free web resource you'll ever come across. It is like getting a free classical music appreciation course taught by some of the best in the biz. Their achieve runs from Bach to Walton and everything in between.

http://www.bbc.co.uk/radio3/classical/discover.shtml

Enjoy!