not really that representative of the Captain, but this is his most accessible and catchy:-

Nick Cave & The Bad Seeds - Loverman
The Residents - Hello Skinny
Tuxedomoon - Dark Companion
Ministry - Jesus Built My Hotrod
English Beat - Ranking Full Stop
Butthole Surfers - Dust Devil
Talking Heads - Houses in Motion (or maybe Pulled up!)
5678's - Eydie Sweet as Candy
John Cale - Pablo Picasso
Captain Beefheart - Orange Claw Hammer
Tom Waits - Jockey Full of Bourbon
Brian Eno - Sombre Reptiles
Cobra Killer - Goodtime Girl
Bill Nelson - Mr. Magnetism
Throbbing Gristle - Persuasion

To name but a few...

I'm picking songs that are well-done versions of bands' typical material.

Collective Soul - Listen
Van Halen (DLR era) - Running with the Devil
AC/DC - TNT
Huey Lewis & the News (a band that was big for a while but hardly ever is discussed) - Heart and Soul