Wrap items in plenty of paper. The paper will help to protect breakable items, but also to fill out the extra space in the box. Filling extra space with paper will prevent the boxes from crushing.
Bag anything that could leak. Then if it does, it won't get on all the other items in the box.
If you're wanting to take any refrigerated items, those can't go on the moving truck. Plan to pack a cooler in your car with these things.
When packing the kitchen, stack plates vertically. Don't lay them flat. They are stronger this direction and are less likely to break
Label every box that you pack immediately. Write on the side of the box what contents are included and which room you want that box placed in at destination.
Have a system for screws, parts, and small pieces. Use a zip-top food storage bag to keep small items together and pack them all in the same box. This way individual bags won't get lost in a larger box.