If you want the results to always be displayed in that order by default you can update the query to add in the ORDER BY at the end of it. When you are entering this into the interface make sure that you click on another selection before finishing in the interface to see if this will make it stick for you.
You could then configure the sorting of the columns based on links like normal and have the results returned in order.
If you want to sort by last_name, then first_name, then middle_name you would just make sure to put these three columns into the columns listing in that order. If two records have the same last name then it will sort by first, two records with the same last and first name would then be sorted by the middle name.