Elvis Costello Armed Forces and TMBG Flood. Basically buying on CD what I already had on vinyl and tape.. I was probably about 15 when I got a CD player of my own (my father had bought one in like 84 when they were super expensive and I wasn't allowed to touch it so I suffered with a tape player and turntable)
They weren't my first albums... The first album I ever bought on my own was:

I was in 4th grade and it cost 7.95 for the 12 inch and I had to buy a needle for the old record player that my uncle let me have too--that ran about 2 bucks if I remember correctly. Money came from my first baby sitting job.
My father owned a music store (instruments) when I was in 4th - 6th Grade and I used to pay attention to what all the musicians who came in said they were listening to then I'd go to the record store once a week with my baby sitting money and by an album or two. I've got some shit 12 inches this way but I've also got some cool things too like Elvis Costello and Pearl Jam and different things that kids my age weren't listening to.
Though I did buy an MC Hammer 12 in and Vanilla Ice in addition to the NKOTB album above so I did buy some shit when I was little.