Subway tile backsplash is classic and would look great. I don't know what the counters are, but if there's any color in them, pull a color from there; you could use it for the backsplash color, or use a honed marble subway tile.

Agree subway would look good. Yes, remove the 4” splash first.

did someone paint the cabinets and walls the cool whites and gray?,,,the floor is so intently warm that its almost like someone was determined to downplay and went overboard w the chalky white and gray walls...... I'd figure out what you want from this before throwing in a backsplash that might be more confusing than anything..... backsplash is your detail but what is the palette going to be as you do various things w your furnishings and get your personality to come through.?? is there going to be stools at the overhang? will the gray walls remain?

as for a specific tile to insert....nothing else likely to change? a herringbone might elevate the overall situation.

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a colored tile, if chosen to coordinate w the bold floor might ease the visual abruptness between all the white and the floor. I like this, but again...do you have a vision for the overall palette ?

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So this is a new house that im moving in. There is a water view from the dining area. one thought i had (if i do the backsplash in the future), was to capture the teal blue from the water and use it as an accent color for the blackspash and some of the furnishings. just not sure how the white, teal, gray, orange brown palette would go. what vibe it would give.

Adding teal to the room will just intensify the orange in your wood floor. I would not commit to such a bold color on material I don't want to change for 20 years or so.

If you add a color, I would keep it pale but interesting. Tilebar.com is a huge source and sends 5 samples for $5. Here are a few ideas with color.
Greens first:

Here are two pretty blues. I like the pale arabesque one the best.

IMO you have a backsplash , what you need is a new wall color not gray. The rest is just decor stuff to bring your style into the space a new backsplash is IMO not the way to do that right now. The rug in the DR is too small and the colors nothing like what you want maybe start there with a new one and use a color from it for the walls,

It looks like you already have a 4" backsplash, so unless you're going to remove it, then don't add another one on top. If you're going to remove it, you could do the countertops as the backsplash or look into some white tiles. Here is a recent kitchen design we did using the countertops as the backsplash:

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