You should lay out kitchen appliance in accordance with how you use them. There's a lot of talk about kitchen triangles but that's an outdated concept that doesn't work well in kitchen where there's more than one cook. Your best served by thinking about breaking your kitchen into zones. E.g. a cooking zone, a prep zone, a clean up zone and a baking zone. Kitchen designers are trained to help you make these kinds of determinations and I advise you strongly to consult with one.

that's a complicated question - it's custom for each client

What are the dimensions of this kitchen?

specifically between the edge of the island and the wall behind the stools? We are working with a similarly shaped ranch kitchen...

As you know, the kitchen overall is not huge, but it feels big because of the open layout. Because it's a smaller space, we only left three feet between the wall and the island on the stools side.