I'm not going to pretend I can list my favorite songs from the 80s, or the new wave, let alone quantitatively order them. Here are jsut some random songs, albums, etc. that I loved and I also thought were influential for good or bad: (in no particular order)
Mirror Man-Human League
Life of Reilly- Lightning Seeds
Veronica- Elvis Costello
Bananarama- First three albums
New Order- Substance (Disc1)
Kiss Me, Kiss Me, Kiss Me - The cure (Entire LP including "Hey You")
Flashdance Soundtrack (Including my favorites song of all time, the title track!)
I Feel For you - Chaka Khan (More influential to 80s pop and the long term of popular music than anyone will ever admit.
Neneh Cherry - The duet of "Buffalo Stance" and "Kisses on the wind"
EVERYTHING BY MADNESS
All Late 80s "alternative" before it became seattle.
EVERYTHING BY MADONNA UP TO AND NOT INCLUDING "Justify my love"
You Spin me round- Dead or alive. The perfect song that just needs to be and need not influence anything nor justify itself.
I Want Candy
All other early eighties sterotypical songs (99 Red Balloons, Tainted Love, Safety Dance, Take on Me, etc.)
All 80s soul music, without which the New Wave would have had no cultural counterpoint.