Build at least twice the size you decide on. Cause you'll end up getting more, and more,and................ I use top rite netting. Knotted is supposed to be better if you are in a snow area. Until size/support becomes out of hand, I like poultry netting. It just seems more secure to me and so far nothing's gone through it. Coons are one of my major predators, so I use 1/4 - 1/2" hardware cloth on the sides, hoping to discourage climbing. So far they both have worked and as long as I remember to lock everyone up at night, I haven't had any problems.
If you may have to lock them in during harsh weather you are going to want a bigger shelter. Also plan to have a quarantine area for new purchases and/or young. Good luck and enjoy.
I agree with extra space...You might end up wanting more varieties and once your peafowl finally have peachicks you will probably want to keep your very first peachicks (at least that is what I did) and so you need space for that, etc. If I could go back I would have 5 aviaries before I even got the peafowl. All 5 aviaries would have top write netting with hot wire around the pens and each pen would have running water inside. I spent a lot of time researching the birds themselves and then pens for them was hardly a thought. When I got my first peaowl I literally threw a dog kennel pen together the day before we got the birds and we put them in there. Then later came a real aviary and then came the learning curve of things that didn't go so well in the aviary and thus need a lot of replacing.