Help us help you. There is more to advice than a description. Post up pics of the area you want to use a backsplash for the best advice.

Backsplash and the kitchen

Of the two you show in the kitchen I like the browny gray one. However I think you can possibly do better. What about a white ( matching to the counter ) in a unique shape. Any shape could work... shell, Arabesque, finger, bigger subway, herringbone .... options are endless. Pretty space

Panel the dishwasher

IMHO color would really make this lovely. You have all neutrals so a pop of color could really make it zing.

It looks as if (picture above) your cabinets have strong horizontal wood grain lines and are very modern. I would pair them with a white glass tile in a 3 x 6 (8"?) inch size (same size as the blue one above) in a stacked pattern. You could try a smaller size like a 1.5 x 6 but less grout lines are easier to maintain. I think the linear look would compliment your cabinets and keeping it white would keep it timeless as well.