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I'd build the frame out of 2".2", fill the gaps with kingspan/celotex, DPM stapled to the outside then shiplap. Recess the electrics somewhere you won't nail or screw through at a later stage. Clad the inside with ply or T&G panels if posh.
The shed market is so competitive if you look around it isn't that much cheaper to buy a half constructed shell that'll be a piece of piss to erect and probably last 20 years with a decent bitumen roof and the occasional lick of wood treatment.
My shed is 8'x8' (based on available OSB sizing) built with 2'x4's and utilizing a "shed" roof (single slope). It has electrical hook ups and is insulated to suit my local climate. Was very easy to erect and has weathered well for almost 25 years.