What material are you looking at for the tops? Slect the backsplash after tops are installed if at all possible.

I'd recommend bringing a cabinet door or drawer front to a local stoneyard, if you can, to view slabs in person and see what looks good with your cabinet color.

If you're interested in white quartzite, do some reading here first because many people have had issues with staining.

Ditto what millworkman said about picking backsplash after the counters are installed.

How did you get this far without having a design plan for the overall look of the kitchen? Dark and moody? Light and bright? Low or high contrast?

What color are the cabinets? Gray or blue?

go to a stoneyard w a drawer front. I would put a stone top on your painted cabinets. a good number will be found to your satisfaction I'd think.

" What color are the cabinets? Gray or blue? ""

They look both to me: a stormy gray-blue. I really like the colour.

OP: You have to know what feeling you want from your kitchen to choose your countertops and backsplash. Plain, busy, classic, avant-garde, shiny, earthy, etc.

Your blue cabinetry is already a strong feature, so I would keep the countertop light and relatively quiet—a white quartz with soft gray veining rather than a heavily patterned stone. For the backsplash, a simple glossy white subway tile would brighten the kitchen and allow the cabinet color to remain the focus.

We used a very similar deep-blue cabinet color in this Torrance kitchen, paired with a lightly veined white countertop, white subway tile, black hardware and stainless-steel appliances. The completed photos may help you visualize how those finishes work together:

https://overlandremodeling.com/kitchens-gallery/traditional-kitchen-torrance-ca

If possible, select the countertop first and wait to finalize the backsplash until you can see the countertop with the cabinets in your kitchen’s actual lighting. Take a cabinet door or drawer front to the stone yard rather than choosing from online photos alone.

Stoneyards have staff there to look at your door and make suggestions. Use that resource.

Blue cabinets usually work best with light tones; pick your counters and then your backsplash. Try bringing a cabinet sample with you to a countertop showroom and they can help you narrow down your vision. https://seremodeling.com/how-to-remodel-a-kitchen 

I would do glacier white Corian for the counter (it's what I have in my kitchen and I love it; I think it would look pretty with the blue and would let you make a bolder choice with the backsplash). I would then do a 3- or 4-inch hex tile from Fireclay tile. They have lots of color options, but I'd avoid anything too white-white unless you have the opportunity to look at a sample with the Corian to avoid the close-but-not-quite problem. You could do gray, or a beige, or an off-white sufficiently different from the Corian to look intentional (ivory, or maybe feldspar).