White-matte cabinets (flat panel, not shaker) and white bench (or maybe epoxy sealed marine ply??...siriuskey can tell you about that), mirror splash. Love the ceilings. I personally would go for a modern, stream-line, no handles, integrated appliances look. This space has real potential to be very cool, even with the slate. It doesn't need any more more texture or darkness. This is a nice kitchen, you should be able to sell it on ebay.

consider a similar colour in a shade darker than the timber trims...if the plinth is exposed to nearby lawn mowing or garden beds the darker colour is more forgiving of dirty marks and makes a better background for planting

As said by big reader...leave white or paint the same colour, without the brushed finish, on the other walls. You can not bring another colour in. There is enough colour already with the orange wood and the bed cover. Also, the curtains look too small to pull right across your window correctly. They should be waved not flat when closed.

I agree with Jan -- a lot is personal , and your lifestyles . You say neutral colours , so a wheat type colour for the carpet is a good middle of the road choice , but maybe not practical with kids who like crayons and facepainting and stripping down motorbikes haha . So in that case , maybe a burgundy or mid blue or similar 'solid' colour may suit better ( burgundy may tie in more with the exterior tones ) , but is still sort of neutral , but what about furniture and linen and artwork -- if you have royal blue or fluro green drawers and a brown chair and sunshine yellow duvet/dooner cover , and the room is for someone older than 4 , then burgundy carpet mightn't be the go haha . The existing wall colour works with most things , you can add artwork or posters or sports or academic certificates -- maybe back to front , but I'd sort out everything else ( carpet , furniture , etc ) before deciding on a wall colour , unless sticking to the existing or similar colour .