Hi Jaymar,
It really depends what use this shed is going to have. If its just for storing a lawn mower and a hose pipe then construction soesnt have to be that great. If its to be an office/workshop then thats a different matter
I build my 16' by 10' workshop from 2"x4" tannelised timber. I built the 4 sides seperately then used coach bolts to bolt the sides together. Much easier than trying to tenon the end of a 16' length of timber! I just used angle brackets to join the frams members (proper ones, not the tiny brackets with 4 screw holes in). I clad the outside in shiplap, 16mm thick, 125mm deep and clad the inside with loft insulation between the frame members, damp proof membrane over that and 11mm OSB as the internal wall surface. 18mm OSB for the floor over further 2" by 4" joists and DPM, and 18mm OSB on more 2" by 4" rafters covered over with roofing felt on the outside. I did consider ply as you suggest, but OSB was cheaper. I surface mount my electric cables in conduit but using 2x4 gives you plenty of room to hide them if you wish, and space to drill through a frame support without weakening it.
This is probably overkill for what it is, but its solid, doesnt move in the wind, watertight and damn warm in the summer! If you want to save on cost 3x2 for the frames would do fine. If its just a storage shed I would leave out the back wall, bolt the sides directly to the garage wall and lap your roof under the garage eaves then seal with sealant or lap lead flashing into the garage brickwork to be totally sure.
Hope that helps!
Steve.