TW is one of my favourite artists. His career can be split in two. His early albums, from 1973-1980 are piano blues and ballads where he has this sort of Charles Bukowski/Barfly persona. His albums since 1983 are a really eclectic mix of rock, jazz, blues, opera, vaudeville, cabaret, funk and industrial.
Rain Dogs from 1985 is a good place to start as it has a broad range of his styles as does the later Mule Variations. If you can get into that you can get into any of his records.
Asylum Years is a good overview of his early stuff and Beautiful Maladies for his later stuff.
I should add that his music goes very well with whisky and a wistful mood!