I want to make consomme. I think I have the general theory down. Im just wondering what veggies works best in the mirepoix, and in what way they should be chopped? I wonder if the French tradition teaches something specific in this regard? 
Do you mean mirepoix?  The standard combination is 2 parts onion to 1 part each of carrot and celery.  See that linked Wikipedia article for alternatives and the related sofrito and Cajun "holy trinity". 