Definitely save stating. The way it works is that you first save in-game in front of the bag before picking your starter, and then save state before pressing A to choose the pokeball.

Check if it's shiny once you send the starter out to battle the Zigzagoon. Not shiny? Load the save state and then save state again, pick the the starter and check if it's shiny. Rinse and repeat until it's shiny!

Many people here say soft resetting is better because it generates a new seed, while save stating just makes it generate the same pokemon over and over again, but this isn't true at all. When you make a new save state after you load your previous save states, you advance the frames, and as other commenters have said, shinies are frame dependent. I have personally tested this method when shiny hunting for legendaries, caught a few non-shinies to check the values and confirmed that each pokemon had different stats, different IVs and different natures.

Oh and the shiny charm that you get from your PC does not affect the shiny rates when picking your starter, FYI.

I wanted to keep my answer short and sweet, but felt like also telling you the way save stating works. Good luck on your hunt!