A little more work, but I went with just the sand at about 6 inches deep. One wouldn't have to go that deep except here (in the western US) we have an issue with the ground "heaving" because of heavy freezing in the winter causing the black earth to freeze and expand (repeatedly) and the deeper sand base eliminates that problem. We also dig a shallow trench at the very edge of the perimeter so the sand will be somewhat deeper at the edges...
I assume you will want to go for the cheapest method. You should use the timber bearers method. We used this method for our shed about 2 years ago. We even used the wood from our old decking so didn't need to buy anything.
Another factor for me to consider is its a very new lawn (less than 2 months) I turned the soil over and laid grass seed in April. This means the ground wont be very compact.
Hammer in fence post holders as below
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saw fence posts to just clear holders, wooden battens crosswise then the shed floor ( make sure it's level) then erect shed on top. Result plenty of airspace under shed. Used this method years ago & shed still solid.
Ron's idea is a good one Boolders. I've done that a few times with decking. 8 should do it. One in each corner, and one along each side, with three joists for the shed to sit on.
Jake's right really... hardcore and a couple of inches of concrete. No need for slabs. No sinkage then (which might happen with Ron's idea, - it depends on your ground.