We have Dulux Endurance paint in our kitchen. It's not at all shiny (I know exactly what you mean) but I can scrub at with a pot scourer ( we still have the occasional wax-crayon on the wall incident) and the colour still stays put. You can have any of the Dulux colours mixed up in the Endurance paint, so lots of choice.
If you do all-white walls, do you think it may look a little stark? Could you do just one wall a different colour? Either limey green again, or a completely different colour?
I am picture mad and the kitchen is open plan with a playroon so lots of colourful toys will be out on floor to ceiling storage. So I was thinking of just using colour through accessories? But good idea about doing a feature wall I do have a wall I can put a bit of colour on which would look good.
What do you think about skirting boards - won't they look silly with slate?
If you are going to put lots of pics up, I would def paint one wall a colour. We've just had our all-white sitting room painted a mushroomy colour, and our pictures look so much better now-it makes all the colours really 'pop'.
I think not having skirting would look v. odd and unfinished TBH.