I'm leaning toward Shiny Eevee since it reminds me of my cat (at least its GSC palette), but Leafeon would also be very tempting! Leafeon is admittedly more cat-like than Eevee and it's easy for me to imagine it basking in the sunlight pouring through the window. (I gave my TrainerSona—anime me—a Shiny Eevee as a nod to my cat, but I've been tempted to evolve it into Leafeon!)
In my mind, IRL "Shiny" Eevee wouldn't be as rare as in-game Shinies—it would just be one of Eevee's several natural color variations (like how Magikarp in the Magikarp Jump mobile game can be purple, grey, etc).