I absolutely adore the SOS mechanic. Good IVs, Hidden Abilities, and shiny Pokemon all in one feature. Before Gen 7, I had never bothered to actually "hunt" for a shiny Pokemon, but it became my favorite postgame hobby in Moon. I've even gone so far as to train certain Pokemon to help hunt for specific shinies.
With that said, the first one I hunted for was my precious Lurantis, which I then used to help chain for more shinies. I now almost have an entire box full of shiny Pokemon.
One of my favorite captures was Alolan Sandshrew, because it took me 3 months to actually find it. What a pain it was too, with Hail, the Snow Cloak Ability, Swords Dance and Gyro Ball. I used my Keen Eye Sneasel to help handle the weather plus evasion (along with Eviolite since it's weak to Steel), and after several hundred Sandshrew knockouts, I finally found her.
Another one I like a lot is my shiny, Modest Nature Starmie with Analytic, which I use in competitive battles.