If you're interested in knowing more about Nick Cave, I definitely recommend you watch the movie 20,000 Days on Earth:
It follows Nick on his hypothetical 20,000th day. It is more or less centered around the Push the Sky Away album. It's a very beautiful, strange, touching, poetic movie.
After seeing this one, stop everything you're doing and run see One More Time With Feeling:
Now this is an incredibly special movie, and it gets a lot more closer to a real documentary than the other one. It was made by Andrew Dominik who is also the director of The Assassination of Jesse James. It follows Nick and the people close to him after the tragic death of his son, Arthur. It talks a lot about the different transformations an artist can go through after a deep trauma. This movie is an incredible, intimate piece of art. It's genuine and poignant. It blew me away.
As for album recommendations, you cannot go wrong with their latest two, Push the Sky Away and Skeleton Tree. I also really like Tender Prey and Murder Ballads. But honestly, if you're new to Nick Cave & The Bad Seeds just grab Lovely Creatures - The Best of Nick Cave and the Bad Seeds (1984-2014). It has all their important music pieces and everything you need, except for the music from their latest album (Skeleton Tree).
A recent song from them that I really like is I Need You: