Classical music newbie needs your suggestions

I admire your quest. This forum may be a bit overwhelming, as most people are listing their personal favorites which you may or may not connect with. 
 As somebody has suggested, you might take a Music 101 or adult education music class to get you started. A good teacher will inspire you with his or her enthusiasm, and guide you on a path of well known classics that have connected to many beginners.

@thomas_vick 

Funny you should such disparate pianists as Horowitz and Gould in the same article. Usually not paired, they’re my two favorite pianists in the world.

You are in for a musical experience  you never dreamed of - especially when listening on a good sound system!  I strongly recommend that you sample the extensive classical selections on YouTube,. The sound quality is surprisingly good with a quality headphone pair, and you will discover many vintage recordings from the golden era of classical stereo. There will be occasional annoying commercials - but the quality and variety of the music is fascinating.

Of particular interest are live recordings posted from Germany and Japan by the YouTube classical community, usually supplemented by worthwhile comments.  I have been particularly impressed with the performances by Charles Munch and the Boston Symphony of works from the French repertoire.  Also noteworthy are the amazing live performances of the Bruckner 7th and 9th Symphonies by Sergiu Celibidache and the Münchner Philharmoniker. Happy listening; your musical adventure is just beginning.

Dear rvpiano, Horowitz and Gould are definitely my two favorite pianist of all time along with Martha Argerich and Rubenstein who played Chopin like no other. 

Rather that rattle off a list of my favorite pieces of classical music (we’d be here all day), I would advise you to do a couple real-world things to inform yourself so you can figure out what you like (of music on-hand now) and what might thrill you in future purchases:

1 - Take the time to read the liner notes. With classical it matters greatly who the composer is (of course) and who the performers are (of course, again) -- but in the larger sense, it matters what era of classical music you’re hearing (ie, baroque style vs classical style vs romantic style vs things that came in w/the 20th century).

2 - And when you hear something that thrills you, note what instrument it is (or instrument grouping: chamber vs symphonic). If you find yourself loving the cello (for example), there were fabulous pieces written for it all over the past 300 years

3 - And finally, note any composers whose works appeal to you, and any performers who impress you most. You can later on pick up more recordings based on those factors.

A friend was here yesterday and really liked a classical recording I was playing (an orchestral piece by Frederick Delius). I don’t know him to own any classical, so I asked, "If you like this so much, why don’t you own any of it?" His answer baffles me: "Because I don’t know enough about it to know what I would like."

All he has to do is spend some quality time youtubing classical of various types and eras--and pretty soon he’d have a very good idea what he likes. Your 300 recordings are the equivalent of that.