don't press the batting, but I do put it in the dryer for a few minutes to get the major creases out.
And no, I don't press after it's together, but I wonder if you are holding down the backing with tape when you first start putting your front, back, batt together. That helps keep the wrinkles out and don't forget to keep it all taut when sewing. Sometimes I take an extra little tug on the back to make sure it is taut when I am quilting.