Start with all their early stuff in this order:
Duck Stab/Buster & Glen
The Commercial Albume
The Third Reich 'n' Roll
Meet the Residents
Not Available
Eskimo
Fingerprince
Their work between The Commercial Album and Demons Dance Alone ranges from "eh" to "pretty fucking awful" (ignore AMG's five-star rating for God in Three Persons...it's really garbage), but you should definitely pick up the album atsonicpark suggested (Title in Limbo with Renaldo & the Loaf) since it's exceptionally good from that period.
As far as their recent output goes, they've been having a major resurgence in quality. You should definitely pick up Demons Dance Alone (a 9/11 concept album, but it's far from cheesey), Animal Lover, and Tweedles.
They have a new album coming up in September called The Bunny Boy, which Mark Prindle told me is VERY good. So yeah, look out for that one.
Whew. I said too much!
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