Pokémon was definitely the starting point for me. While most of my other friends were busy obsessing over The Backstreet Boys and N*Sync, I... was off playing Blue (my first game) with my brother and his friends. XD Then one day I stumbled across a VHS tape of the series at our library, and immediately recognized Pikachu on the cover so I decided to check it out. I was completely hooked from then on.
I never really paid much attention to the animation (I was what, 8 or 9?) but I knew it looked different than the American cartoons I was used to. About that time, my brother discovered DBZ so we'd watch it a lot together. Then there were the other shows like Outlaw Star, Tenchi Muyo, Sailor Moon, Digimon, Monster Rancher, etc. that were aired on TV. I can't remember how I found out they were all from Japan and called "anime" (which I pronounced completely wrong)... but I think it was from a magazine.
As for manga, Magical Pokémon Journey was my very first. I was obsessed with it so much. XD; Then I got hooked on the, er, heavily edited Toshihiro Ono series that Viz released. I'm pretty sure that Tokyo Mew Mew was the first non-Pokémon manga I bought back in 2003.