The first album that I bought was a .25 yardsale cassette of Fleetwood Mac's Rumours. No case or album art. I couldn't even tell you why I chose it but I was absolutely hooked when I popped it in my tape player when I got back home.
If we're talking full price CDs from the store, my first was Californication by the Red Hot Chili Peppers. My dad told me not to waste my money buying an album for just one song. I had to insist that there were 3 songs that I knew I liked and I wanted the album to see if there were more. There were, in fact, a couple more songs I liked but, if my memory is right, I only really listened to the first half and then really disliked the second half.