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First shiny I ever saw was Weedle in FireRed, tried to catch it but I was a stupid kid back then and killed it accidentally with my overleveled Charmeleon
First legitimate shiny I caught was a Bidoof of all things in Platinum. Also had a shiny Nidoqueen in SoulSilver.
Most recent ones I've gotten were from Masuda Method in Moon, along with the Shiny Charm (though I was breeding for comp mons, not shinies specifically). I've gotten a shiny Ribombee (in a Love Ball too!) and Charizard this way. Also found a shiny Fearow in the same game, but that was a wild encounter.
Sadly, the only shinies I still own are from the recent games, since my previous PokéBank account got deleted from inactivity ages ago.