Thanks to @WeMakeMags for the scan of this classic Life in Hell strip. I'm still undecided as to which of these types of dad I'll be most suited for. I'll probably aim for Fun, but come across as a delicate blend of Snooze and Goofy.
For those of you unfamiliar with Life in Hell, it's the rather smashing strip with which Matt Groening made his name. Entirely written and drawn by him, there's a lot more of him in it than in The Simpsons or Futurama – he is a master of daftness. It's endearingly doodly, in a good old-fashioned pen-and-paper way. Plus it was used to sell Apples, way back in the 80s.
A good place to start is The Huge Book of Hell, although as he's recently retired the strip for good, it's possible that an online archive of all the strips will appear at some point soon.