Not the poster you asked but I'd say.. Start at or near the beginning. Later stuff has some gnarly sounding synths and arrangements that might not sound all that palatable to the modern ear (very 80s).
For me I first heard him via his album "Songs of Love and Hate". I found it in my dads record collection after a funeral of a close family member.
It's still my favourite.
It's not modern instrumentation. It's a Technics arranger keyboard like the kind you might have heard in an airport smoking lounge. He started using them because they allowed him to build an arrangement without the help of other musicians. They've always sounded chintzy to me but they worked for him because of the cabaret nature of his songs.
Pretty sure I first found out about Cohen (and Pixies!) via Pump Up The Volume (1990). Fantastic movie. I thought the Concrete Blonde Everybody Knows cover was good, but then I dug and found the real thing and was blown away..
FWIW I think they're comparable, but just very different. Johnette Napolitano's voice is fantastic, and she really gets to stretch out on "Everybody Knows". As good as the recorded version is, hearing Concrete Blonde do it live was amazing. I saw them in 1993 in St. Louis and that show is still in my top 10 concerts, ever.
> synths and arrangements that might not sound all that palatable to the modern ear
Are you referring to I'm Your Man? Because I'd say that it's his single most accessible collection of songs, and that his adoption of modern instrumentation was a genius move. The backing track for "First We Take Manhattan" sounds like New Order!