off the top of my head:

Dead or Alive - You Spin Me Right 'Round (Like a Record)
Level 42 - Something About You
Simple Minds - Don't You Forget About Me
Spandau Ballet - True
George Michael - Father Figure/One More Try/Faith/etc.
The Smiths - How Soon Is Now?/There Is a Light That Never Goes Out/etc.
Talking Heads - Once in a Lifetime/And She Was/etc.
Soft Cell - Tainted Love/Where Did Our Love Go?
Peter Gabriel - Big Time/Sledgehammer/Games Without Frontiers/Shock the Monkey/etc.
David Bowie - Let's Dance/China Girl/Fashion/Ashes to Ashes/etc.
Grateful Dead - Touch of Grey
Moody Blues - Your Wildest Dreams

Also, The Police, The Cure, R.E.M., U2, and Tears for Fears all have too many songs for me to list.

That should be a fair kickoff selection.

Good choices with Whip It and She Blinded Me with Science, btw.