I didn't have a turntable as a kid, my parents had one, and got into tapes in my early teens, mostly Dead bootlegs. So my first album would have to be the first CD I bought, which I bought with no CD player to play it on. "Standard Time: The Resolution of Romance" Wynton Marsalis.
I wasn't even really into jazz at that point but the wine shop I worked in sold off some CDs for $1 each so I bought it. Great album and got me heavily into jazz and I still have it.