In about 1959 when I was 13 - Mozart: Symphonies No. 40 and 25 with the Philharmonia Orchestra with Otto Klemperer conducting. Yes, I would still buy it again and if I ever see a re-issue I'd snap it up in a second.
8 years old - First 7" single: Chicory Tip - Son Of My Father (1972) [Buy it again? Er... no]
12 years old - First LP: Little Richard - Little Richard Live (K-Tel 1976) [no I wouldn't, it's nadiresque]
23 years old - First CD: Lloyd Cole & The Commotions - Mainstream (1987) [I still have it]
I have spent the last 10 years doggedly tracking stuff down from my childhood & youth - backcataloguing I believe is the term. One of the most exquisite moments was finally stumbling across Spliff - Spliff Radio Show (1980) in a second hand CD shop in Amsterdam in 1999 after having it itching away on my frontal lobe's wish list for about 12 years.
Most of the records I have were presents or part of a collection my sister's godmother was giving away. I think the first one I bought myself may have been "Le Petit Prince", an audio play that I bought at a flea market in France when I was a teenager. The first LP I remember owning myself (and having asked for) is a recording of Bartók's violin concerto and the two rhapsodies for violin and orchestra that I got when I was 8. I asked for it because my sister and my brother were playing the first rhapsody, and it was my favourite piece at that time. I remember that I was a bit disappointed because the recording was with orchestra, not piano. I still have the record and still love the music, although I don't mind anymore that it's with orchestra. 🙂