I would not go with white. I would go with an off white subway with your favorite color in the quartz countertop as the grout color.

Have you actually looked at all these materials together? Shades of white are very difficult to work with and have them actually look good together. Many times one will make the other or others look dirty or faded or dingy. Personally, I am not a fan of multi shades of white.

Here is a photo with white subway tile- If you choose to do white I would do some sort of accent tile to pull out the other colors in the tile & countertop. If you choose to do a subway tile without an accent tile I would suggest doing a crème/or brownish colored tile to pull out the colors in the flooring/countertop as well

I feel like the counters and floors already coordinate, so you don't need your backsplash to carry that load. Just go simple -- an off-white if it makes a livable combination with your white cabinets, or else a light buff tone that coordinates with the counter.

You may want to check out Pratt and Larsen hand made tiles for the backsplash. We did a similar installation using Taj Mahal quartzite and used a solid textured tile from Pratt and Larsen in a light taupe color which would pick up the subtle variations in the stone and the floor. One of the great things about this company is they have many colors to choose from and can even create custom colors. You can look on their website to find a dealer in your area. This also looked great against the white cabinets.

We have attached a link for you to check out the textured subway size tile.

http://prattandlarson.com/product-category/field-tile/textured-field/

We have Taj Mahal quartzite and used Waterworks ice water color crackle glaze tile in 2x6 subway tile for our backsplash. We are very happy with how it turned out.

You need to consider all of your elements, floor, counter, cabinets, backsplash and walls.
Your tile floor looks pink, your counters look like they have gold. Very hard to tell over a computer screen. Are you working with a kitchen designer. Highly recommend you get some help on this. There's many shades of white cabinets and many shades of white tile backsplash. Be careful it does not become too bland, all light and mid tones. You need some contrast, maybe a dark floor or countertop?