I'd go with blue, white or silver gray.

I would have poo poo’d this idea before as I’d wonder what the point was, but make your self a mood board using the colours roughly in the same ratios. Are you planning on having some artwork as this may be the lynchpin that helps it hang all together. Pulling colours through from that will help the scheme. Tonal can be soft and soothing but needs layering up with texture to create a cohesive scheme. Alternatively pops of bright colour can look amazing and your kitchen is lovely and bright with good bones. What is the rest of your house like, and what is your style?

I would consider what time of day you use it and clarify if you want to lighten it or make it warm. 'Cool' colours such as greens, violets and blues look cold if they are pale so avoid these if you want a cosy feel unless you use dark versions. Warmer colours are recommended for North facing rooms, but it is really down to the other components in the room. No use choosing a warm grey unless it works with the new carpet. The carpet will cost more than the paint so I would select both together.

Pick out a colour from the rug. Can I see orange?