Wow... saying "recommend me some classical music" is like saying "recommend me some pop music". There are lots of different types of classical music and it really depends on what you like. "Classical music" is really divided into several different "eras" or periods:
Rennesance(sp?) Period (Gregorian chant)
Baroque Period (Bach, Handel, Vivaldi, Pacchabel)
Classical Period (Mozart, Beethoven)
Romantic Period (Tchiakovsky, Chopin, Brahms)
Modern Period (Debussy, Copeland)
I'm just throwing these out off the top of my head....I'm sure a google search would get you a better breakdown of eras/composers. The least you need to know is that each era is defined by a particular and unique style. Here's a quick breakdown:
Renasance(sp?) Period (single line melodies, generally without harmony until later)
Baroque Period (Harmony is explored more fully, pieces are very "mathmatical", without emotion, and very ornamented with lots of trills and such)
Classical Period (Music begins to become more artful and crafted in a more emotional way, yet still very musically "correct")
Romantic Period (Art supplants musical "correctness" in importance and all harmonic options, even dissonance, are on the table for maximum emotional impact)
Modern Period (all bets are off... do whatever you want. There has been sort of a return to the Classical style, and also a movement towards "Nationalism", e.g. Copeland's pieces sound very American old west)
For listening suggestions, I'd second Bach's Brandenberg Concertos. The Amedaus soundtrack (mostly Mozart) is another great one. There are lots of "Best of" CD's out there that can be a good place to introduce yourself to classical music. Generally you can't go wrong with: Bach, Mozart, or Beethoven. They are the big three. Buy yourself a "best of" disc from every composer I named above and you will have a darn good start.
Two things will probably surprise you: 1) how much classical music you already know and will recognize, and 2) how cheaply you can buy classical CD's.
Good luck,
A