I second Buzz on draining the tomatoes.
A good double fine strainer, OXO for me, will yield clear water from 6 in 1. From Chicago, all the sauces I have had has had a biting fresh taste. I wouldn't recommend heating the sauce, the oven will take care of that part. For a chunky puree, 6 in 1 is the best, or whole plum tomatoes torn up by hand in a colander will do. Chicago style for me is a dry, greasy crust, and sauce as thick as peanut butter.