Please, no white subway tiles!

are the walls staying that green color? If so, then all of these options will work. (if the green isn't staying, let me know and I"ll post others)

This Portmore tile in the shades of green would look great w/the wood.

do it in a herringbone since everything is very plain and solid.

since it's a lake house, what about a soft green glass tile? No gray.

Tilebar, Loft Aspen, 2x8 glass tile

or something w/a print or shape?

This is called Tidewater. very pretty (Tilebar, Cadenza line)

This one is Byzantine Latte and looks great w/the wood cabinets. (Tilebar.)

byzantine in the Blue:

ming green marble tile

handmade type of zellige tile in a soft minty green

If you're up for repainting the walls a lighter, white color, (which I think you could) then try this beautiful blue/green zellige tile. blues and greens all look great w/your wood.

light blue, ivy hill tile.

I'd prob do a soft white wall though.