The author of The Rest is Noise has put together playlist of modern music as an intro to classical music listeners who have never heard anything written since 1900 or so.
A look at many big city orchestra programs won’t reveal too many of these pieces or composers. I’m not sure what to make of it all either, but if he’s going to the trouble of assembling a playlist, I can give it a listen. Only $19.80 stands between you and enlightenment, as well. It looks like I know one of these pieces pretty well, as I like Sibelius a good deal. And I have heard of a few more, but by no means all of them.