As with most artists, the 1st 3 albums are seen as his best with it trailing off after that. Still a lot of good stuff but not as consistent.
The Fine Art of Self Destruction is probably his most accessible.
The Heat is now probably my favourite. The cover is a bit of a homage to Springsteen's Darkness and you can hear it in the album.
Glitter in The Gutter is his LA album, certainly his most rocky and was expected by many to push him up a level. He had a minor hit with Broken Radio (duet with Springsteen) but it never really happened.
There's a live album, a good covers album which sold better than any of his other stuff and a Best of. His latest was produced by Lucinda Williams and features her on some tracks as well as Billy Joe Armstrong.
If you want to go deep, he was in punk bands Heart Attack and the relatively successful D-Generation before going solo. There's also an album by Bellvue that was released between D-Gen and Fine Art that I really like, it includes some of the stuff he later recorded solo but heavier/punkier versions.
Forgot to add The Finger - hard core punk band with Ryan Adams, perhaps best swept under the carpet now.
tldr: The 1st 3