Hi marjproops,
Not an easy situation for you, especially as your DC is autistic and likes stuff to be readily available. I imagine DC is very attached to many items and won't enjoy the whole upheaval. Although the transition to a new home will be difficult, I'm sure with your obviously excellent parental skills that DC will adjust well. It maybe a good opportunity to go through everything,and sort out what is important.
Depending on size of DCs bedroom, could you put a bookcase in there for some of the books etc, (storing heavy ones on the lower level, as don't want anything too heavy on upper shelves.) If money is an issue, try local papers for a cheap book case (or my local charity shop has a furniture section and they make deliveries for free; I know some people are sensitive about using Charity Shops, but they are excellent, its amazing what i have found there in the past.)
Maybe you could put a desk in DCs new bedroom? or do you want to keep the areas for work/play separate? Both my DDs have desks in bedrooms, (one desk is actually a dressing table but it fits the space), the desks have a little set of drawers which they love for their stationary etc.
You will need to be inventive about about storage, you mention the possibility of a garden shed, so I assume new place will at least have a garden. I have a garden storage box full of toys, balls, play tent, bottles of poster paint, craft material (chalk, sequins, buttons, pipecleaners etc). I store individual craft material in plastic boxes or ziploc plastic bags (so I can push the air out and seal the bag, it saves space) I then put these bags/boxes in a larger plastic crate which I can easily put in/out of garden store. As craft stuff is well wrapped, there hasn't been any problem with damp or mould.
It also is fun to use the garden for craft, then DC can make as much mess with paint and glue and you don't need to worry about carpet! Obviously not very practical to work outside in the winter, and last summer was pretty poor weather wise.
I use dining table for a lot of my DDs craft work, but it is a pain having to clear everything away, especially when they are the middle of a project.
Invest in a few large plastic boxes, keep a different coloured box for different activities, so DC will know where everything is, and then you can move boxes around the new house as needed. Buy the boxes before you move, then it will give you and DC a chance to sort out material, and may help DC adjust to new place better if they then already know where there things are.