You may think that the most logical way to pack your plates is to place them bottoms-down into the box. But actually, plates are less likely to break if they're standing on edge inside the box. Of course you also need to wrap each plate in newspaper and include plenty of stuffing on the bottoms, sides and in the corners of the box. Put so much stuffing inside the box that the plates don't have any room to shift around at all. Generally speaking, when you're packing glass items, you should pack the largest glass items on the bottom of the box and the smaller, more delicate glass items on the top of the box. Movers aren't always delicate with boxes and if they plop one down on the floor or the ground, the glass on the bottom of the box is going to take a beating, so those items should be stronger.
If you're using professional movers, consider having them pack your fragile items. Companies are usually only liable for the things they pack themselves. So if they pack it, you're essentially insuring it.