I don't recall the song, but it was a 45 by the Go-Go's (wasn't willing to buy the whole album because I had never heard of them before). Before that my collection was made up of LPs and 8 Tracks.
As for Xanadu, I got the full LP back then, and have both the CD and DVD today.
My first LP was Sgt. Pepper's Lonely Hearts Club Band, and the first 45 I owned was Eleanor Rigby (my mother gave it to me). But the Go-Go's 45 was the first I ever purchased for myself.