Wash your backing and iron it before you quilt. When you wash your completed quilt, use a color catcher just in case some of the colors on your top bleed. Nothing like red, black or turquoise bleeding onto white or a light fabric to ruin your quilt. It is best to wash your quilt in the bathtub because agitating the quilt in a top loading washing machine can make your quilt a wonky shape. Gently squeeze the water out, don't wring it! It is best if you can sandwich the quilt flat between 2 sheets out on the lawn to dry as hanging will really stress the quilting and seams because a wet quilt is heavy!
I always wash and iron my fabrics before I cut anything to make a quilt. I want to get rid of the chemicals used on them to keep the bugs off in the warehouses. I have read in some quilting magazines that the fabric manufacturing companies are putting more chemicals in the fabrics now because the fabric is staying on the shelves longer.