I would start with one of the tables first, you will need some place to put folded fabric before you have space on the shelves. As you fold stack by color. This will make it easier to organize later. Don't worry about ironing anything now, you can iron and refold as you need it. After table is folded, empty cubby onto table, place a stacks of folded, color sorted fabric in cubby, fold fabric on table and repeat. You may need to move some of your color stacks around a you go. Keep a trash can and a box for non fabric things that need to be put away close. At this point you are only concerned with fabric but when that is all done you will be surprised at what you have found hiding in the fabric. LOL By the looks of this you should be able to fold it in a weekend. If you stop to put away other things, or clean as you go it will take longer. I would set a timer for 1-2 hours take a break, have a cup of tea. Good luck, getting started is the hard part.