Full size.

4" going to the sewer, the house is getting a half bath, wash machine in the basement, kitchensink, dishwasher on the 1st floor and full bath on 2nd.
I've added up 19 fixture units which can be handled by a 3" waste in Massachusetts. I'm not sure if the inspector will want full size from the waste going out to the sewer which is 4". Can I just put a no-hub adapter, cleanout and then transition over to 3"? Or do I have to keep it 4" all the way up and out?

sewer

You can probably run 3" to a point outside the building, but you should install cleanouts where you make the transition, otherwise you will never be able to snake the 4" pipe using the 3" one.