I usually don’t iron until right before I am ready to cut. I wash and dry in the same way I will wash and dry the final garment. When I am not lazy I pink the sides first to cut down on stragglers, but mostly I just throw it in!
Before cutting, I straighten up the fabric to the grain thanks to a tip from Cynthia Guffey. I fold the fabric selvedge to selvedge and make sure it all lines up. If it’s not exactly right, I pull on the fabric at the corners and stretch it a bit until it is. I hope that explanation makes sense. It is really a step that has changed my sewing. When I have taken care to make sure the grains are lined up correctly, pattern pieces line up when I do this! I tend to use cheaper cuts of fabric for lining, and they tend to go off grain a bit.
For knits, I have sprayed cut pieces a bit with starch and ironed, and that has made them a bit easier to work with. BUT, you have to be careful ironing that you don’t stretch the fabric.