Others have given great advice on coop size, etc. I'd like to address your predator situation.
With cougars and bears, geese won't be much protection. You need to incorporate hot wire around the coop or you will invite a bear to destroy it and clean out your entire flock. Cougars will be happy to pick off your chickens as they free-range, so be aware that you may face more than just losing an occasional bird to a predator. You can get cleaned out in a single day.
I have faced this problem myself. Early on, you may see no predators. But eventually, they will discover your "meat market", and you will likely experience significant flock loss and infrastructure damage, the latter being as devastating as flock loss. After battling bears and bobcats, I finally installed hot wire with a solar charger around all my coops, runs and gardens, and I've had no damage or loss since. It's very simple and not expensive to install.
It's foolish not to plan this system of protection from the very start of your endeavor. Your predators will be "trained" from the beginning and not get into bad habits that will be hard to break, even with hot wire. Peanut butter dabbed on hot wire at intervals sends a "message" that once learned, will discourage predators for years.