Bought with birthday money from grandparents...had my parents take me to Musicland to pick it up.

If we're being strict and have to stick with albums we bought with hard earned money, then it would be Metallica's ...And Justice For All.

Duran Duran and Ratt's Out of the Cellar, both bought at the same time. My sister bough the Footloose soundtrack that day, her first album.

<font color=lime>The first music I bought was Ratt, Invasion of Privacy. It was a tape. :D </font>

System of a Down

The first CD I bought for myself was when I was 10 yrs old...I bought Spice Girls: Spice World.
Yes I know shameful :(

the first singles (yeah i'm old) I bought where the Boomtown Rats "like clockwork" ... safe punk and Lindasfarne "run for home" prog rock trying to be pop.

Ride the Lightning -- Metallica (late 1990)

In fact, I still have that album, all scratched into oblivion :D