My extended family is full of musicians, and as far back as I can remember, we were always going to bluegrass, country, polka, and folk festivals/concerts, but the first individual artist I can actually recall was Conway Twitty, not long before he died.
As for the first real rock concert? I won a pair of tickets by calling a radio program for Megadeth, Fear Factory, Flotsam & Jetsam, and Korn (on their first tour).
The first tickets I ever paid money for was to go see Primus with my girlfriend at the time. Primus sucks, and so did she. That particular show also had a pit more dangerous than anything I'd encountered before; not even Slayer was as bloody.
But the first time I ever went completely solo, was to go see B.B. King. I heard the man was in town last minute, had a cat inside who owed me, and was pressed into temporary bar-back duty and listen to the warm up jam that B.B. did. Tiny venue, huge legend, it was fucking mystical.
In between all that, I ended up at the first Detroit Electronic Music Festival, which was also my first outdoor daytime electronica experience. Prior to that, it was all underground warehouse parties.