Aah, here comes "the K-tel Challenge" 
Choose from one of the following:
a) put together a would-be "greatest hits package" from whatever alternate universe where Our Bearded Hero is world-famous and any average no-talent singer on our pop radio is stuck working at the local Soylent King
b) choose 'sampler' songs that showcase the many different styles that encompass the great melting-pot we currently enjoy as the current body of work.
I think perusing the discussion thread where we board-goers discuss the songs that got us hooked on JoCo would be very helpful in this task. Of course the more you look the more you'll find nuances in the similarities and differences of the various peoples' musical tastes.
When making sampler CDs for friends of other artists ('Rush' is a great one to do this with) I find it's important to pick songs that showcase all of the things they are capable of (i.e. I lean to option 'b' above). I'd choose a couple songs from the first album, a couple from the 2 EPs, and a smattering of things along the TAW path.