Considering the cabinets and appliances are retro, I would keep with that idea for the tile. The glass is a bit to current and dates everything else that much more. Stick to more natural colors that blend with the cabinets, maybe a stone looking 4x4.

Neutral tile backsplash and not the one that is leaning behind the stove. The color looks off.

Penny rounds and new hardware.

You can glue tumbled stone 4x4's directly to your drywall. The edges are finished enough so you won't need trim. If you don't mind snipping the corners, you could an a few bronze 1x1's. Don't overdo.

White subway tile would compliment the floor. Search it on this site and there are loads of pics.

Thank you for all the suggestions! We are planning to replace the appliances and were not going to use what is in the picture. Thanks!