2x2? May aswell crack out the Lego.... I'd do the frame out of at least 3x3 depending on size.... and then the side cladding and roof from 3x1. Maybe even 4x4 and 4x1.
Are you building it like the one in the picture with the divider? Looks like 4x4, And sorry, I meant 4x1 for the roof.
Looks like 3x2 for the uprights, sounds ok, as for making the rest of it, follow the drawing above and just make it up as you go along sort of thing? Any out door stuff I do like this is always done that way, design and think as you go sort of an affair. I would make sure the roof is well on incase the wind lifts it. You could ply the roof and cover it in felt(mineral green) maybe? The last one I did comprised of just a roof as above with a few legs, lean to design and approx 6ft high at the highest, slanting out and down to about 5.5ft, it was 4 ft deep and 12ft long. It holds a transit load of timber built, MAX,(Box transit, 16'' pieces just fired in). In the summer the plan is to fold up legs sideways under roof, and roof then folds down flat and plumb with wall, and out of the way. The legs do need to be anchored to the ground, little steel tab in ground, pin goes through leg. That way the wind cant lift it when in the erected position. Im not of much help to you here really to be honest, all Id say is make it fit as much as you have room for(If your allowed!) And concentrate on making nice lookin as you go...
Would i be right in saying to make the ends and middle first then join them together with 5x1 etc etc?
Finally got round to building the smaller one of the two I require: A morning with these bad boys as per TSC recommendations: And it's looking like this: For anyone into chopping wood, get yourself one of those Fiskars Super Splitting Axes! They are the dogs danglies!