Their feathers should be in at 2 1/2 to 3 months in which time the weather should be decent by then.
You have plenty of time to think of a design for your coop, so don't worry. I have even seen some large dog houses converted into some nice coops. Just as long as it is safe from predators and gets them out of the elements. If you know anybody that is renovating you can snag some free building materials, and really cut down on costs. I got some nice used 2x4s that way one time from a business next to where I worked. They threw them in the dumpster, so I borrowed a truck and took them off their hands. They are now the roost bars in my coop. My ex-husband would come home with windows and all kinds of stuff from construction projects he worked on. They were just going to throw that stuff away!
I'm glad you get to at least hatch your little ones! I hope your family lets you keep them after all your trouble of hatching them. I think once they see them, it will be a no brainer. Babies are hard to resist and not fall in love with.