for fantasy books I would suggest Patricia McKillip.
She's amazing and has won the world fantasy award twice.
I would suggest Ombria in Shadow, Forgotten Beasts of Eld, The Changeling Sea, and/or Winter Rose (those are my favorites)
Patricia Wrede is good too, Mairelon the Magician and Magicians Ward are good. And of course her Enchanted Forest books (there are four).
The Only Alien on The Planet and Breaking Rank are amazing books by Kristen Randle, theyre not fantasy but modern and about real things.
For classics I would say Jane Eyre, its my favorite and an amazing beautiful story. Pride and Prejudice, anything by Charles Dickens or Shakespeare, Tolstoy, just walk down the classic section at the library and start picking.
Oh, and the Chrestomanci tales (there are two book) are really good by Diana Wynne Jones (fantasy not classic).