I'd recommend white grout throughout. Seal it well!

The lightest of silvers looks better over time. TEC PowerGrout in 909 Sterling. Never needs sealing. Never fades.

I like to match each tile. White grout for white grout and blue grout for blue. If the blue tike goes nicely with the white tile you don't need any grout colors to tie things together. You can use white for both which us more commonplace likely because it's simpler and easier to do. But i like a striking contrast that compliments which you will get when the blue tile has blue grout as well.