That's a pretty tiny little shed. I think 2x4s would eat up a lot of internal space. 2x3s would likely suffice. What are you going to sheath it with?
Suppose you used a 4x4 at each corner and a 2x3 or 2x2 midway between (maybe 2 of them on the long sides. Sheath with OSB. Screw it on so as to form a solid skin. I think you'd be in good shape.
The idea with this is just to make it cheap. How it looks is irrelevant. But it does need to be sturdy and dry. I was going to cover the whole lot with OSB and then maybe even felt the sides as well as the roof.
The one on the right, that is. Note no sole plates on the end walls. Lay down the floor before you put up the walls and toe nail the end wall studs into the rim joist through the flooring plywood. There'll be nothing to step over at the doorway, as well. You could make the door a bit taller. I copied your door and just lowered the header above it.
Leave the floor and roof as you drew them. The floor could be 2x4s roof could be 2x3s.
How about building it up off the floor so it doesn't rot?
And some blurb from their website...."The building had to be rot free and allow good ventilation - we employed the Walter Segal principle and have raised the building on stilts to ensure an even air flow around the building, should rot occur all is needed is to replace the feet themselves. This system is now quite popular in our products and we are presently building a scout hut on National Trust property using this principle. As well as the obvious benefit of reducing the likely hood of rot is the fact that the ground is not disturbed unduly still allowing good drainage. "