Sure, there was such a melting pot of stuff, I myself never went much for genres, preferred originals that were distinctive. Indeed, some bands changed so much as they became famous that some people may never have even heard some of the darker earlier music - Simple Minds spring to mind in that category, possibly Psychedelic Furs too.

the next band will be fairly obvious! ;-) Gotta get some classics out of the way at the start.