I would get 7 and label them Sunday, Monday, Tuesday....  That way you empty one to eat, load it and run it.  Organizing by type means that you have to wait until you've used very dish and utensil  you own and run them all at once.  You'll need an extra sink to stack dirty dishes in until they're empty.    

--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.