The first CDs I got for my first CD player? Why, Blind Melon and the Jurassic Park soundtrack, of course.
After that, I got Dookie, the Blue Album, Soundgarden's Superunknown and Pearl Jam's Vs. I had a crappy CD boombox in my room that I'd lay in front of for hours, listening to music over and over again and making mix tapes from the few CDs I had.
I also had a small CD shelf that held maybe 50 CDs that I would obsessively organize and reorganize everytime I got a new CD. I created a vague hierarchy of merit, with my favorites going up top and it going down based on how much I liked each band. I'm pretty sure I also signed up for a couple of those CD clubs and stretched out actually paying the full $18.95 for the CDs for as long as legally possible in order to acquire my first batch of CDs.
Those were the first CDs I ever bought myself. But if we're being completely honest, the first music I ever owned was a cassette of Gloria Estefan and the Miami Sound Machine, which I got as a Christmas present and was super fucking excited about. What can I say, the only music I was exposed to at that tender young age came from hearing stuff in the car with my parents, and my parents have terrible taste in music.