1980s also produced some "underground" stars such as the Go-Gos and The Cure...this culture of music is known as Modern Rock and here is more about it...
The first and foremost collection of Modern Rock you can find is a dual CD pack called "Modern Rock" by Timelife Music.... It has really good old favourites like music from Duran Duran and the song- "Oh Mickey, you're so fine you blow my mind...Hey Mickey...." so this CD is not just punk rock favourites, it just doesn't pay attention to 80s Hair Bands....
Step2
Build you own collection of Modern Rock CDs or Casettes and remember casette singles? Once Again, I give the advice of going to the Goodwill to sift through and find entire albums by the likes of Cyndi Lauper and Information Society....
Step3
Burn a CD of Modern Rock... I do not burn CDs because I don't know how but I still listen to old CDs burnt for me that actually had the Punky Brewster theme song along with the Care Bears...it was a very ecclectic sample of television show 80s Modern Rock...