The backsplash is great. Look at your photo and see that there is definition between each tiles but not too dark. I would select a grout that will do this as well. No white, but a medium to light almond or taupe grout. Hold up the plastic grout samples to see which works best. Hope this helps.

Match your grout to your tile so the tiles seem to become one piece. We did that with our backsplash and floor, and it was amazing how the right color of grout knits it together.

I would use the same color as the tile so it appears seemless.

It depends on if you want it to be seamless or not? Do you want it to appear as one piece or do you want it to be linear? Grout can change a lot. See the photos below.