First, make sure your kitchen is organized. Tupperware goes here, the lids go there like this, glasses go here, plates go there, flatware gets sorted in this drawer, etc. If a child knows where things go, and there is organized storage, that will help.
When my first was born, dh and I had quite a lot of Pfaltzgraff dinnerware and place settings. We liked it, but it's heavy, chips easily, and isn't very practical for a family with a young kid (if you want that kid to help out eventually).
When he got old enough to participate in setting the table, clearing, and then moving on to loading, unloading the dishwasher, we switched. Packed up the Pfaltzgraff, and started using practical dinnerware that was lightweight but not ugly. It would almost bounce if dropped. We did have nicer place settings for holidays and special dinners, but for the every day family meals when the kids were expected to participate in table setting and clean-up, we just used unbreakable things. I'm not talking about paper plates, but acrylic, etc. Saves a lot of headaches.
So if you're petrified of broken dishes, is it because you are using dishes that can't be replaced, or are you afraid of injuries? Figure that one out. Figure out how to give your kids the tools they need to learn the skills they need.