I have what I hope are some structurally sound plans for framing the walls with 2x4s (is framing the right term?) the four corners are 4x4s. I could take pics of my plans if you want. Local library is closed for covid but I will see about ebooks.
4x4s are NEVER straight. They are also never 8' or 10' in length. You will have to trim them to size, which means two cuts from your typical 7 1/4" circular saw. That's a pain. Also, you probably don't need PT wood (as most 4x4s are) in your corners, unless you plan to use them as supports to hold your coop of the ground. (I did this, its not a bad plan, but you will need to go thru all the lumber in the yard looking for the straightest 4x4s you can find, in both planes).
If you aren't using your 4x4s as legs, I'd recommend 2x4s and a "california corner" instead - much easier to get the wood to square up nicely, and ultimately a stronger construction. (Picture stolen from internet, better than my crude sketches)