How many eggs you looking for? That determines the number of birds........about a dozen eggs a week from 3 to 4 birds. Then 4 sf or so per bird. A sturdy 6' x 8' or 8' x 8' coop would be good for a dozen birds and about 3 to 4 dozen eggs per week (when they are laying).
Anyway, if your home is already built, that would be a shame as most likely there was enough scrap left over from that to have built an appropriate sized coop. If not, a nice one can still be had, and even more so if you are able to do it yourself. Keep it simple and build it sturdy.
I do not have a run. I built a predator tight Woods coop (8' x 12') that is oversized for my 9 birds (it could house about 20 or so), but no run. If they need to stay in, they stay in. No harm comes to them there. But when I let them out, they have room to roam but are confined and protected by an electric fence that cost less than a large run would have and opens up about 50X more space than a run would allow. The coop protects them from things that go bump in the night and the fence confines and protects them during the day.