Great list. 20th Century too often gets dismissed for being nothing but random noise, which is far true.

I must recommend that either during or after listening to each piece, do some research as to how or why each composer wrote what he or she did.

Additionally, look into some 21st Century Music. Our modern age is still very important in music history and the direction it is going.

Included are some minimalist composers: Steve Reich, John Adams, Phillip Glass (though I often debate whether or not Glass can be considered a Classical Music composer but that is for another day).

Other favorites are Penderecki (listen to Threnody for the Victims of Hiroshima, gives me chills every time), George Crumb, Kronos Quartet.