The first shiny I ever caught was a Fearow in Pearl (it was also the only shiny I got in Moon before I restarted)
The first shiny I ever bred was a Shinx in Black
The first shiny I ever SAW (also in Pearl) was an Absol, my absolute favorite pokemon at the time. However, I had no idea what a shiny was and was like "why is this one red?" I don't know why I didn't try to catch it or if I DID and took out all its HP on accident, but when I look back at this memory, I get sad.
I actually have a lot of shinies, either from trading or breeding, and very few from actually finding them. The one I'm proudest of is a shiny Moltres that I ended up getting in Heart Gold. I accidentally KO'd the Articuno (my favorite of the birds) and didn't save prior to it (I would have had to re-play about an hour or so to get back to where it was, and I wasn't about to do that), so for Zapdos and Moltres, I was sure to save before the battle, as I wanted to catch them. I accidentally KO'd the Moltres a few times, but when I reset one final time, it was a shiny!! Needless to say, I made sure to catch it, even though the shiny version looks like a plucked chicken and is definitely not one of my favorites.
I also bred for a shiny Zorua for MONTHS. It took so long, but it was worth it. Shiny Zorua is so awesome looking.