Mink are hateful! I lost three chickens and a drake duck to a mink last February. It is amazing how persistent they are and how small an opening they can squeeze through. Go forward with your hardware cloth plan. I made aprons around my runs and coops, and I added Nite Guard solar-powered lights. I don't know if the lights really work, but I enjoy the additional peace of mind of believing I've added a layer of protection.
I also have a pair of American Buff geese. They are great watch dogs, and they make a lot of fuss, but I wouldn't trust them to physically protect my other birds. Gussie and Golly are my first geese, and they co-exist with the ducks and chickens (although everyone has their own house at night), but the geese are inseparable. I think having a pair is a good idea. I bought mine at the local Bomgaars, and although I didn't think about making sure they weren't both male goslings, I'm pretty sure I got one male and one female.
Never hesitate to ask questions here; people are always willing to help you when they can. Welcome to BYC!