Do I build a shed out of polystyrene bricks or not?
Yes but no..
Build it, but not out of polystyrene..
1) On most sites the simplest foundation will be a rigid reinforced concrete raft. You can pay a hefty sum to a structural engineer to draw up a specification for you, or deploy a slightly over-designed 200mm slab specification that I've used several times on some pretty horrible soft clay soils, without any problems:
i) Clear the topsoil down about 9" from the surface. The surface below needs to be level and compact - you can hire compactors, also known as whacker plates. If the soil below is dry and not claggy you can set the concrete directly onto the subsoil, otherwise add a small amount of fine hardcore (usually scalpings) to level the site and assist compaction.
ii) Order enough A252 (8mm bar, 200mm x 200mm spacing) reinforcing mesh to place two layers of mesh across the slab. Where mesh sheets meet, allow at least half a metre of overlap. Thinner mesh will work, but it is springy and easily displaced when you make the concrete pour.
You can get little supports to keep the mesh layers clear of the ground and clear of each other, but half bricks work just as well. The steel must not come within 50mm of any surface of the concrete, else there is a risk of blistering (aka concrete cancer)
When ordering your mesh, also order a couple of 6m sticks of 12mm rebar to help support your shuttering.
iii) Never underestimate the ability of freshly poured concrete to push over shuttering! Get some 12mm shuttering ply cut into 200mm wide strips, then with a few blocks of timber, screw together your shuttering cage to support and form the edges of your slab. Also cut your rebar into half metre long pins with an angle grinder to drive in to support it. Make sure the shuttering is level and square - use the 3-4-5 triangle method to check the corners, and ensure that the pins are driven fully in (or cut off if not possible) so your tamping board is not obstructed. Make sure the shuttering is fully sound and rigid before ordering your concrete.
iv) Phone round your local ready mix concrete suppliers to find the one who can deliver the quantity you need at the best price. Don't try forming a reinforced slab with an ordinary cement mixer - it's very hard work and doesn't give a good result. The grade of concrete you want is called C25. You may want to include admixtures to delay setting time, or achieve a degree of water resistance - discuss with your supplier. Fully waterproof concrete is very costly however.
Consider how you are going to get the concrete to the site if the mixer can't drive right up to it. Concrete pumping trucks are fairly expensive to hire, but work really well - they can easily articulate over the roof of a house and deliver concrete accurately in the garden behind. Barrowing concrete may be an option, but you will need plenty of labour (and builder's barrows) as it's very hard graft.
Order enough to complete the job, and a tiny bit besides. Have a good use lined up for the leftovers, as concrete trucks need to completely empty themselves.
As the concrete is poured, have rakes and shovels on hand to help spread it, and then start tamping straight away. You need a good straight rigid plank for this that can span the slab - eight by two is usually favourite. Tamping has to be done by two people - one on each end with the board on edge. Keep working back and forth until the slab is nicely level.
After the concrete has gone off, don't let the surface dry out too quickly, especially if the weather is hot and dry. Use a watering can to keep it damp, but not too soon or you'll mess the surface of the slab. Keep an eye out for your pets as the concrete is setting - make sure they don't leave a permanent impression with their paws!