Because the heat from a gas cooktop can damage quartz with its 36% by volume resin content, you can't get anyone to recommend it behind your cooktop. If you want tile, it is most often run down to the countertop. Plus, because of that you don't need to pick a tile until sometime after your counters, cabinets and led lighting are in place. This way you can evaluate samples in your space.

Stove wall: Tile only; no short quartz piece with the tile. Take the tile all the way up to the bottom of the hood. Like this:

Sink wall: No backsplash. You don't need it, and there's no way elegant way to place it; it's going to look like a weird strip of tile running down the length of the wall, and you certainly don't want to detract from the nice view you have. I wouldn't even do a short 4" quartz splash because the stove side won't have it if you go with tile on that side and it will look off. Just paint the entire wall area on that side and be done with it. Not every wall needs tile or a splash.

The purpose of a backsplash is primarily to protect your cabinets, floors, and subfloor from water and your walls from cooking effluents, so you might find a backsplash is needed in both locations. On the sink wall, consider using quartz up to the bottom of the window trim. That’s enough to give you the protection you need, and it keeps the window as your primary focus. On the stove side you can use tile in the space under your uppers and vent hood. I would choose a tile that harmonizes with the lighter background color of your counter material.

Don't under estimate the visual interest of fantasy brown, especially with your floors. You won't need a lot of extra visual input.

What color are you painting the walls? I see no reason for tile behind your sink wall and think paint is just fine. On the range side, I'd tile potentially tile just behind the range or on that whole wall beneath the cabinets.

The purpose of a backsplash is primarily to protect your cabinets, floors, and subfloor from water

Can you say more? I see the counters as what protects your cabinets and floors. I see backsplash as decor. Paint has always provided me protection from heat and cooking splashes behind a range.

@Kendrah, since you first came to houzz a few years ago you’ve been touting the adequacy of paint as a backsplash and I’ve been explaining why it’s not enough. We’ve had this exchange so many times, perhaps you could read my previous replies. Or just Google it. Thanks.

I have never heard of a manmade ”Quartz” named Fantasy Brown.

Do you mean to say ”Quartzite” which is a natural stone?

Apparently FB is closer to a Marble from what I have read from the stone experts here.

Here is what I would do on the sink wall. Add some wood shelves and tile just to the bottom shelf and then under the window sill. Put the FB countertop in the window as the sill instead of wood. Something like this?

The Stove wall is easy. Just tile up to the bottom of the cabinets and hood. I probably would tile above the MW shelf up to the short upper cabinet, but that is up to you.

Below are some kitchens we have designed for our clients. You might notice how we used all the same backsplash in each design. Notice where the backsplash ends in each around the hood vent and the windows?

Lafayette Luxe Kitchen · More Info

Lafayette Luxe Kitchen · More Info

Parisian Elegance · More Info

Wine Country Charm · More Info

Wine Country Charm · More Info

The difference is, OP has no cabinetry on the window wall. Anything other than paint is going to look awkward IMO. Rebunky's idea isn't bad, but the edge of it where the tile would stop is too abrupt.