You can stay neutral but use different textures in the tiles. Glass mixed with ceramic or marble is good. I would put tile on the entire backsplash and make a great accent piece over the range. Change up the patterns also. It will add interest without adding too much color. If you want to be bolder, chose one or two colors in the tiles that you can live with or that you have in the rest of the house. That will pull your color scheme into the kitchen and make a cohesive look as you go throughout the house.

Could you provide some picture of what you have so far? From what you have described I would probably go with a warm grey or light brown to match the veins in your floor. Good luck!

Do you have any pictures you can post? Actual names of the products/colours already chosen? That would help to ensure any advice is appropriate.

I would use a brown glass subway tile and as for paint that will depend on what is in the rooms next to the kitchen a couple of pictures of the space and the arch would help.