I just finished one section of a two-section 8x8x8 coop. Each section is 4x8 and 8' high. I put all of my framing together with 2x4's (1 1/2" x 3 1/2") using a large box of 8 x 2 1/2-inch, Phillips Square-Driv Deck Mate Premium All Purpos Exterior Screws and my Rigid 18-volt drill. I bought everything at Home Depot.
When putting the plywood or osb boards on, use the shorter deck screws or wallboard screws. I bought a large box of 7 x1 5/8-inch, Phillips Square-Driv Deck Mate Premium All Purpos Exterior Screws.
Remember, too, that the stores have large saws that will cut your panels and boards you buy to any custom size you need. That can save you a lot of time, and their machines/saws are deadly accurate with the cutting.