Your getting great advise and awesome pics to help you decide. If you need to along the way, you can tag me (@wrathsfarm) and I can try to help.... Close to 30 years in construction.
Like posted earlier using torx screws are a little more costly to start instead of framing nails, but the...
Fyi... Check to see if your local Lowes has a cut station in their lumber dept. This could be a big help once you get your plans/blueprint/material list of the coop finalized if you needed it.