1st off I don't wash my fabrics but I do dip them into my home-made starch solution and hang them up to dry. Then when dry I take them down to dry iron but I do have a spray bottle to mist them a little. I find they come out better if I don't use steam here but I do use steam when I'm pressing during assembling the blocks. Also when I acquire my fabrics I check them for flaws as most of my fabrics are purchased online, then I fold them onto comic book boards and put them in their proper shelf. I might press them if I find they are very wrinkled from shipping though.
You'll find some folks wash their fabrics before using, others don't. You just have to find out what works for you. I used to wash and iron mine years ago but got out of that habit because I didn't need to go thru all that work. With starching and pressing the fabrics before cutting I find some shrinkage has already taken place plus I find out if the fabric is going to bleed when I dunk them in my starch solution. My backings are the only things I don't put thru this method so might throw them into the dryer with a wet rag to help shrinkage them before use.