LOL. I won a copy of Black Bear Road (the album that contained the song "Convoy") by C.W. McCall when I was a kid -- and come to think of it that might have been my first album. It was either that or a Three Dog Night Greatest Hits album I bought because of late night television commercial. Good times.
Cassette? I do not recall. But if Cheap Trick's At Budokan wasn't my first cassette, it was close.
Compact disc -- Communique by Dire Straits
Download -- I have no idea. It's interesting that I have at least partial recollections of my first LP, cassette and CD, but none whatsoever of my first download. And I'm sure it's at least in part because buying and listening to an LP (or a cassette, or a CD) was always more than just about hearing the music. You were also checking out the artwork, reading the liner notes, looking at the songlist, learning who played the instruments on the songs, discovering who wrote the songs, etc., etc. With downloads, click a mouse and two seconds later you have music but not much else. It's not the same experience.