I don't remember the first album ever, but I remember getting my first CD player when I was twelve and ordering one of those special bundles from Columbia House, which included (I think):
Eagles - Greatest Hits
Eagles - Greatest Hits 2
Steve Miller Band - Greatest Hits
Paul Simon - Negotiation & Love Songs compilation
CCR - Chronicle
The Lion King Soundtrack
Yanni - Live at the Acropolis
Enya - Watermark (my mom's request)
k.d. lang - Ingenue (also my mom's request)
...and more. I forget if there were 10 or 12 total. And the ones my mom wanted are among my favorites today, go figure.