The first shiny that I ever encountered was a Teddiursa back on Gold. I only had high-leveled Pokemon with me at the time, and I ended up KOing it even with a weak move.
The first I caught, though, was a Shiny Shroomish on Sapphire. I don't even remember finding it, but a few years later when I was checking my boxes before I restarted my game, I found it sitting there. I ended up trading it to my Fire Red, and then transferring it to Heart Gold where it still is today!