Our family is the same size as well. We use china. I usually do the dishes. Winter time is torture with the water so cold, so sometimes I would prepare a huge pot of hot soapy water and use that to wash the dishes and glasses. All the kids get dishes, but little kids get plastic cups. I have large goblets and they are hard for little ones to hold.
Also, the thought of all those disposable plates filling up landfills, would make me feel guilty using.