My first experience with the franchise was when in 1999 when I was eleven. First I bought a magazine that had a Super Smash Bros review, and was puzzled about what this new character called Pikachu was supposed to be.
After that in France we had promotional comic books released and given away for free at Toys'R'Us stores. Each comic book was an episode of the anime in comic book form and three or four articles about the games. And that's when I started to be interested, more by the game than the animé. I did start to watch the animé, but remember losing interest around episode 6 or 7. A few months later I got to try the game on a friend's Gameboy (I didn't have one back then) and was immediately hooked. I got a Gameboy Pocket for my birthday in 2000 and Pokémon Blue a few weeks later.
After that I tried following the animé again just to see what treatment different gyms would get in the animated form (just like reading a book then watching its movie adaptation, you know) , but I gave up rather quickly and ended up hating the animé with a passion. I still love the games though.