TOD:
As much as I fondly recall certain early LPs and books, etc., I don't believe I can say which ones would have been the first that I specifically bought with my own money. I can bring to mind a few that I know I bought, but they are probably nowhere near having been the first ones.
I do, however, know the first piece of music I ever bought, though probably not with my own money. The big deal was that it was also the first time I took the bus by myself, all the way down Main St. from the Bexley area to the then-wonderful downtown Columbus, Ohio. I was nine or ten, had discovered Gershwin, and was thrilled with the Concerto in F (Eugene List/Howard Hanson recording on Mercury, still a favorite) which I longed to play around with at the piano. My mom called one of the big music stores (Summers & Son), who either ordered or had a copy of the piano solo arrangement, and off I went one afternoon. (Everyone made a big deal then of how this little kid came in all by himself for the Concerto in F.) A few years later I graduated to the "real thing", the two-piano score, and eventually the study-size orchestra score. Sadly, while I think I still have that original solo piano version, I somehow lost those latter two fire engine red beauties along the way. I'm thinking my parents probably paid for music I needed for piano lessons, but I remember when I discovered Broadway vocal scores and started ordering and paying for those myself.