I didn't get my first CD player til quite late (had to survive off cassette tapes rewind/ffwd and the radio) but at the time I was given my first CD player it was the Olympics (I think this was 1996). I um cringingly liked the Gloria Estefan song from the Olympics ('Reach'), so I bought her CD album with this song on it. I bought the Spice Girls album next along with the Soundtrack to Romeo and Juliet (I still like the majority of this one)...and then promptly got rid of the Spice Girls one at a school charity donation as I hated it so much.
Before then it was anything recorded off the radio/anything I 'borrowed' off my sister or anything my parents wanted me to listen to (bearing in mind I was a kid/tweenie/early teen then). I think that ranged from Barry Manilow to Peter and the Wolf to Bryan Adams to Richard Marx to Times Tables on tape to story books to Disney soundtracks to The Fresh Prince to Boyz II Men etc.
My favourite favourite 2 songs as a wee kid (like, 4 or 5) were 'La Bamba' and 'Ghostbusters' (oh and 'La Isla Bonita'). Boy I could have played those over and over again on the turntable.