Here is an idea for a simple shed door, we built this a couple weeks ago to replace an old rotted door.
I install these with the same 1×4 layout on the back as well as the front. Then I use coated 1-5/8 inch screws through the front and back. This gives it more stability but it is still not really heavy.
One of the neat things about this design is that you can use a 1/2″ sheet of plywood siding and it still holds itself rigid.
We caulk the seams and screw holes and paint it. Everything together comes to less than 90 dollars, including the latch, hinges and paint.
Happy Door Building!