to keep the chairs on the rug, even when you pull them out to sit - I would suggest you choose the largest member of the family to try it and someone else measure around to see what size is required (it's usually between 30 and 48 inches larger than the table ) ... round or square would maybe depend in what else is in the kitchen in my opinion ...

this link might help too !!
http://www.houseplanshelper.com/dining-table-size.html

10' x 10' , I would not put a rug under a kitchen table it will get filthy in no time.