I wrote this the other day for gaf:
I think Murder Ballads is a good place to start. It's got variety, and the content is around-the-board interesting.
The three albums before it, Let Love in, Henry's Dream, and Tender Prey are all excellent. Tender Prey seems to be considered the best of the three, although I personally think Henry's Dream has the best songs, and Let Love in the best production. Note that these three albums are pretty similar when it comes to quality. It's difficult to go wrong with either one. The only reason I recommend Murder Ballads first is because it has more immediately interesting subject matter.
The albums before Tender Prey are also all very good (The Bad Seeds are insanely consistent when it comes to quality output), but they sound rougher and the production isn't as good. I'd recommend checking them out if you end up being sold on the band via later albums.
The albums after Murder Ballads have the band moving into pretty disciplined, often quieter, singer-songwriter territory. This was a very nice development for the band--post Murder Ballads, it seemed like Nick's songwriting changed a bit; became more internalized and much more personal. He was always a great songwriter, but it's like he found a new level of maturity as he grew older, like the craziness of Murder Ballads was him getting something out of his system. This period has produced the worst album in his career (Nocturama, whose only real crime is being kind of. . .par and nothing more), but it's also produced The Boatman's Call, No More Shall We Part, and Abattoir Blues/The Lyre of Orpheus, all of which different people claim to be his best album.
The also have a great rarities collection and a pair of really great live albums.
