Obviously I'd need to learn how to play an instrument first, but how would I learn to read music? Should I just start taking music lessons? Would it be unreasonable to be able to want to play Haydn, Wagner, Mozart, Bach, and Beethoven in 5 years? I'm learning towards the piano right now.

You could do it, but it would take serious dedication.

You could learn a handful of songs by rote, but to actually comprehend the music you are reading and play with musicality (not just pressing the notes) it's going to take awhile.

Take a beginning piano lesson and see what you think. The concept of reading music is pretty straight forward; marrying that to Mozart coming out of your hands and understanding the theory behind the chord structures is quite a bit more complicated.

You could just do like I did...get a guitar & just figure stuff out while picking things up here & there from friends.



But if you actually want to know what you're doing, you should get lessons on your instrument of choice.

Get lessons.  As far as your repertoire, those are great choices, but after 5 years you'll probably be on Mozart and some Bach.  Keep in mind that to do it "right", you need to get the technique down first and then the music is secondary.  In regards to "classical" music, the technique is what sets you free.  You won't be able to play musically and express what the composer intended if you don't have the "chops".  I've seen too many people fumble on instruments because they think they'll improve by learning pieces instead of technique.

Where do you live?  When getting lessons I have a couple tips.  First and foremost, check the teacher's resume.  Piano and guitar are two instrumetns that a TON of hacks "teach".  Just because some old lady has a piano and a shit-load of students doesn't mean she can play or teach...same with guitar.  Don't be afraid to shop around and compare.  Since you listed some serious rep that you'd ideally like to be able to play in five years or so, look for a teacher with a MINIMUM of a masters degree in music PERFORMANCE on their instrument from a good music school (if you live in or near a major metropolitan area, this should not be a problem).  DO NOT, I repeat DO NOT go with an "ed" major.  You need a specialist, not a jack of all trades master of none.