Here is a video of our basement which includes the kitchen/bar. This was completed roughtly 20 years ago so styles have changed but we combined cabinet styles using wood as the common element. Door, drawer pulls were also consistent

https://youtu.be/3FqMEqaf0-I?feature=shared

Since you already have white cabinets and will be adding the white quartz countertops, you could easily do the quatz as a backsplash. If you are wanting to add some color though, here are some ideas for you for backsplash ideas. You can mix metals in this basement kitchen, but you'll want to make sure everything else works together well before selecting hardware or pendant lights (if needed at all).

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If you're doing white quartz as countertops, you might just run that up the walls as the backsplash. If you can't do that, try a simple white tile. Notice the countertops and backsplashes used in these kitchen designs of ours:

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