Well it should have been either of these three in Glasgow back in 79/80: Numan (at the Apollo), Magazine, and OMD (at Queen Margaret's I think). I had a ticket for all of those, but having no pals to go with, and once having also been a shy lad, I bottled out!
First 'band' I ever saw live was at a dub heavy reggae performance in Leicester in '81 (where I was a student at poly). It was a very grass roots kind of event which initiated me into the bone trembling sonic's of heavy bass.
First proper 'name' band?
Well, that dubious honour goes to
Bauhaus. Saw them in ('81, I think) at Leicester University De Montford hall.
The gig had all the lights up beforehand and a lot of cut-up mashed tapped music playing out loudly, and I think as I recall, Bauhaus kept all the lights on during their set. Perhaps I'm wrong there, as being Goth you'd expect them to keep all the lights down...