Not sure on my first, but one of my early gig memories was Terrorvision at Rock City in Nottingham, supported by a little known band called Feeder.
Best gig, tricky.
Moby at Greenbelt Festival in 1997, he picked up a guitar and played an awesome version of Purple Haze.
Nickelback at Hammersmith Apollo in 2004, first gig with my wife.
Foo Fighters at Earls Court 2005
John Mayer supported by Newton Faulkner at the Royal Albert Hall in 2006 I think.
Big Bad Voodoo Daddy at the Jazz Cafe in 2002 (if you're into big band swing jazz)
So many good bands/artists to see. You can't beat seeing someone live, especially in a small venue.