The first piece of recorded music I personally bought myself was not an album. They were cassette singles (cassingles) I bought from Wal-Mart in Miamisburg, Ohio in 1991. They were Mariah Carey's "Someday" and "Emotions" with "Vanishing" as the B-Side. I still really like the early Mariah Carey stuff, up until and including her MTV Unplugged performance. But I don't really like stuff her after that.
I don't know for sure what the first album I bought was since I didn't have money and they were usually bought for me as Christmas or birthday gifts, such as Bryan Adams Waking Up the Neighbours, Janet Jackson janet., and The Spin Doctors Pocket Full of Kryptonite.
I do remember in the 7th grade, my favorites cassette albums were Green Day Dookie and Boyz II Men II. I had such a crush on Billie Joe Armstrong from Green Day.
As far as the first CDs I bought: I felt like the last person in America to not have a CD player in 1995. I babysat my neighbor's children during that summer and used the money I made to buy a CD player and some CDs. The first CDs I bought all on the same day were: Hole Live Through This, Nirvana Unplugged, Clueless Soundtrack, Alanis Morrissette Jagged Little Pill.
I still really like all of the above mentioned albums and singles. Although when I first bought Alanis Morrisette's album, it wasn't played to death. I bought the album before it was huge. It actually debuted at no. 118 on the Billboard charts but now it's one of the best selling albums in history. So after a couple months, it was played so much and after a year later, several other songs were played a ton. I ended up selling it since I felt I didn't have a need for the CD anymore. But a few years later, I ended up buying it again used since that CD really is a great listen from start to finish. But I was just sick of hearing it on the radio and MTV all the time.