Do you want to know how museums sort out a collection like yours? ONE Rule! = Same things together!
First estimate the volume of it all, and get enough cardboard boxes to hold it. - Don't worry, you won't keep the boxes, they are just for sorting.
Stand the ironing boards up to help clear space. or use them for sorting tables. Start by clearing the fabric out of the storage cabinets and sort it by color into boxes - do not be surprised if you have 12 or more color categories. (I have 24) Leave the tops open.
Now you have a place to put your all of your non fabric stuff!!!! Notions, patterns, scissors and cutters. Get clear plastic shoeboxes, and put them on the shelves, and sort the notions into them. remembering, "Same things together" Like thread, or ribbons. You might not leave them there, but after they are sorted, they need a place just to be!!!!
Do this until you get a rough sorting of everything. Batting is a third category. Bag it in clear bags and put it all together too! Fill up a closet to the ceiling with it just to get it out from underfoot, if you can!
NOW, you can work on arranging where you want things to go!
Remember, you have to have enough storage shelves to hold all of your fabric and notions, because they can't float in the air.
Good luck! Hope this helps! Feel free to PM me ! I am a retired museum director, and am glad to help! jpthequilter
PS forgot to say -
give away or sell what you can,
Buy a couple of rolling racks to hang as many of your quilts as you can.