First record I bought with my own money was the 45 single, "Take the Long Way Home" (Supertramp). I saved up some quarters to go get it. It was 99 cents and I had four quarters and my dad explained to me how sales tax worked and that I didn't have enough money yet. We had to wait for me to do some more chores.
I think the first LP (cassette) I bought with my own money was Bryan Adams Reckless. A few years later I remember buying Run-DMC Raising Hell cassette with my own money - I felt very subversive and independent when I walked out of K-Mart in Mandeville with that tape.