That's an awesome idea. Lots of color, texture, robust surface for grime, etc. I'd glue 'em down using a siliconized latex adhesive caulk. (Siliconized latex caulk has more adhesion than plain latex caulk, but is much more removable later than pure silicon caulk. An example is a product called White Lightning 3006) Run a generous bead on the inside half inch edge and a zig zag down the middle then press firmly against the wall, checking that they don't shift. This will hold them fine but is also removable later with care. Just make sure the back sides are clean, for the adhesion.

What appliance finish(es) do you have or are thinking to use? How high will the backsplash be & will it continue behind a range? What type & tint of hardwood floors - lighter/darker than the cabinets? A few or a lot of windows & natural light in your kitchen? Have you picked a sink, fixtures or wall color? Is the kitchen open to other areas you want to coordinate finishes or color schemes? And - what "mood" do you want? Without a larger context, I can't see the actual space... Hard to interpret from such a small tile of marble - reads as a splash of milk against the sublte (and beautiful) granite slab & milk chocolate doors. At first glance I thought it was too much contrast, but the palette grew on me the more I looked. Not a typical choice, but might be lovely. Envision it with a section of marble or milkglass shelves on metal brackets, antique white linen or lace simple window shades or shutters, milkglass or marble cabinet pulls, milk or caramel glass light shades...sophisticated & understated with a timeless flair. This could be very sleek & charming. The foggy grays in both materials soften the contrast. Since they'll be on different horizontal/vertical planes & if the marble only shows hints of veining as the sample does, I don't see the veining movement of the two surfaces competing. A wood (floor/cab or inbetween) or metal narrow shelf molding above the marble might help tie it all together. Safe & expected backsplash choices would be more of the same granite (especially if you anticipate leftovers & your fabricator can slice it thin for a backsplash), gray or warm tan glass in a continuous sheet or glass/ceramic tiles, metal or a manmade thin solid slab. What makes your heart beat faster & lifts your spirits? Tell us more!

Have you thought about stainless steel backsplash tiles? https://www.houzz.com/products/4x11-honeycomb-matted-metal-peel-and-stick-backsplash-tile-set-of-3-brushed-st-prvw-vr~100903589. These tiles would look great with your stainless steel appliances.

OH BOY. I'm sorry I know you must be unraveled, but realistically it looks more like the counters dont go with your kitchen as they are brown tones and everything else looks black white and gray. Why did you leave the granite backsplash up? that would help minimize it a bit I think.. We need to see the whole room.