Punkfolkrocker - there are electric guitars and fuzzboxes on a couple of tracks on Broadside.

As to where to start - I'm a big fan of the band and my favorites in order are Broadside, Hedonism, Burlesque, EPOnymous, Matachin.
There are some great tracks on Matachin - Fakenham Fair is one of my all time favorite songs of theirs - but you can tell they didn't have a producer!