Well, if they've already got a Nebula or Hugo nomination (or award) they generally make it to my reading list eventually. Of those you mentioned, I was only really aware of Mieville (which appears to be the youngest, incidentally?). And Stephenson, obviously.
I suppose it comes down to taste, but holding up Neal Stephenson of an example of someone that's not an "overrated old guy" strikes me as odd. Granted "the Diamond Age" is great, and "Snowcrash" is great fun -- but after he got so famous editors didn't dare cut back on length (It what it *looks* like happened, more likely he's a voluntary victim of modern publishings idea that many words must be better than the needed amount of words) the novels go kind of down hill.
I recently re-read the foundation trilogy and was pleasantly surprised at how well the characters had stuck with me over the years -- but I suppose some will feel his style is too simple.
On a side note, the sci-fi book I generally recommend people to read first is "the Stars My Destination" -- but I must admit part of what makes it stand out to me is how early it was written.
For any *actual* library 54 books is a little light to represent sci-fi as a genre -- and I'd hope they both fit in Lem, Strugatsky (btw, see http://rusf.ru/abs/english/ for free downloads) Bradbury, Gibson, Sterling, LeGuin, Kress, Vinge as well as newer authors... but I'm hard pressed to list anyone a generation younger than Sterling off the top of my head.