Comment by jzb

I'd start with The Future (1992), I'm Your Man (1988), and Ten New Songs (2001). Those are, IMO, his most accessible and there's a very good chance you already know a few of those songs and haven't realized you know those songs. (e.g., "Everybody Knows" from I'm Your Man has been in a few movies, as have "The Future", and "Waiting for a Miracle" from The Future.)

Note that there's a really stark difference in his voice starting in the mid-80s. His early stuff doesn't sound quite right to me because I equate Leonard Cohen with his voice in the later albums.