Probably the Ninja Turtles movie soundtrack on cassette, which I got way before I ever got to see the movie, and as I had recently seen the film Grease and was young enough at the time to not really understand the distinction between musicals and regular movies I assumed that all the songs on the tape were musical numbers performed by characters in the movie.
Pretty soon after that it was Cool as Ice by Vanilla Ice, and I also remember buying a copy of 3 Years, 5 Months and 2 Days in the Life Of... by Arrested Development from a friend. I had a slightly odd and embarrassing pre-teen phase of listening to middle aged solo male artists for a while after that; Bryan Adams, Peter Gabriel and for some bizarre reason I remember owning a copy of the Mick Jagger solo album Wandering Spirit - I think because at the time one of his songs was getting a lot of airplay on MTV. Most embarrassing of all is probably having a copy of the East 17 album Steam

But that was all when I was a very young kid and didn't really have a developed taste as such. I consider my first
actual single and album purchases that I bought with my own money - on CD no less - as Hey Dude and K by Kula Shaker, shortly followed by 1977 by Ash. The latter I still kind of love to this day. The former not so much (though I still have a nostalgic fondness for it).