Auraninja
Eh, ragazzo!
Funny, for me it would depend on characteristic, and since all IVs are tied, I'd use the special characteristic to choose.Gender also matters- I found shiny Eevee from FS some time ago and it was girl so I decided to make Vaporeon of her since I already have Sylveon and Umbreon my favorite shiny Eeveelutions. If I would find said Eevee now I would probably make it Espeon if it's girl and Jolteon or Flareon if boy.
HP- Vaporeon
Att- Flareon
Def- Leafeon
Sp. Att- Espeon, Glaceon
Sp. Def- Umbreon, Silveon
Speed- Jolteon
Or something like that...
Edit: And congrats, AquaRegisteel. I actually got a shiny Dustox myself, but I caught it with Wurmple. I believe it was Bold, so I was happy it evolved into Cascoon rather than Silcoon.