The very first band I liked was ABBA. I was around 7 years old and loved a ABBA compilation record an older cousin had.
But the first band I became a really big fan (wanting all their records and so on) was The Beatles, when I was 14.
I listed to a radio special about the 20 years of Sgt Peppers Lonely Hearts Club Band where they played the entire record. I was hooked! Got the record as my birthday present and that was only the beginning of my obsession.