First of all...yay for you! Lots of choices then!
But, even though daunting....I would wash what you have. Some materials just aren't "feeling good" in a quilt. But that is just my opinion. I wouldn't bother ironing until ready to use it, unless it comes out of the dryer exceptionally wrinkled.
Wash what you have. Buy foam boards (or get unused cardboard things from the quilt store or Joann's) and place them on the bolts. Get some heavy duty shelves and put them on there. If you are worried about dust, try a shower curtain on a rod to cover. Will help with sun-fading as well.
Personally, if I can't see the fabric I have....it's out of sight out of mind.
I would do it by color with the exception of holiday fabric. All my Christmas stuff stays in a group because I don't want surprise santas showing up in a quilt for the middle of summer just because it happen to have the right color red
LOL
It WILL be a LOT of work. Do you have a quilting friend that could maybe come and help you? Have an organizing/folding party?
I'd help....but you'd have to have diet coke on hand