Hiding spills and dirt on the kitchen floor doesn't seem like a good idea. A small rug in front of the sink would be OK.

I think the material is more important here than the color. A flat-weave rug is easier to clean. The rugs marketed for indoor-outdoor are a great choice because the fibers won’t absorb spills, or you can go for a smaller rug that fits in your washing machine. I would also consider a non-slip rug pad to prevent accidents while working in the kitchen.

The color is a personal choice so pick whatever you feel comfortable with. Neutrals are a safe bet but your kitchen is already in neutrals so it asks for an injection of color. I would pick a colorful rug with some pattern in it to give life and warmth to the space. Pattern is also a good choice against stains by the way. Good luck with your shopping and please add a picture when you decide. I am curious what it will look like. :)

I would say you don’t need a rug at all. Visually, you have enough pattern with that floor. And from a practical standpoint, a kitchen rug is one more thing to clean. And depending on the rug and whether you have a large front loader washing machine, you may have to take it to the dry cleaners. You don’t even have the kitchen rug yet, and you are already showing reluctance about the spills on it that will happen in the kitchen. It doesn’t matter if the rug is dark - it will get a matted, grungy look from drips and spills regardless. Whereas a floor you just wipe with a damp sponge, finished.