White

The grout color that best matches the tiles; contrasting colors show any and all uneven install work.

Has he seen the tile and counter together ? Mixing whites can be tricky and for sure when 2 different materilas are used. I might be tempted to do the vein color for backspalsh with matching grout but we need to see the kitchen to really advise. I do not like white grout but at least make sure it is epoxy type.

white, the same color as the tiles. Texture rather than pattern.

white, closest to the tile shade.

White. Ask the tile setter to do a sample of the grout on a wood board so you can see it before it’s permanently placed in your bathroom.

Correction: kitchen.