My comments about run roof and floor are based only on my own experience in CO, which is the only place I've kept chickens. Our runs are chain link panels all the way around and supported chain link on the top (it is heavy and will sag, we used posts attached to the top rails and crossed, with readily available chain link fence hardware and fittings, cutting the posts to the lengths we wanted). Our main predator concerns here are birds of prey, fox, and coyote, as well as neighborhood dogs and the occasional skunk, but if you have weasels of any type, chain link will present little challenge to them. My recollection is that they mainly hunt at night so if the chickens are securely closed into the coop at night you may be okay. If the run is going to be in the sun in summer, you might consider shade cloth during hot months. We put it up every spring and take it down every fall, and it has to be attached pretty tightly with heavy duty zip ties because we get pretty nasty wind here, probably not as great a concern where you are.
We have used gravel over the ground in some runs, and I have my reservations about it, because of the difficulty of shoveling poop/snow without taking the gravel along with it. The big *but* is, if you have any drainage/flooding issues at all, the gravel will be worth the hassle.
The other thing you might want to consider is, before you add any birds, consider treating all surfaces with mite/lice control - permethrin should work, it's relatively affordable, and you can get it at the feed store and just mix in one of those pump sprayers you would use for the garden - if you do, make sure to mark the sprayer if you have multiples so you don't use it somewhere you don't want the permethrin (it will kill bugs you do want as well as the ones you don't). Do two treatments about a week apart. Don't let cats near the permethrin, it is dangerous to them.
If it was me and I had a baby and a full time job, I'd probably just get pullets at least the first year, see how you adjust to having a flock. I love the boys, love their crowing, the way they call the girls over to treats, and how a good one will be a wonderful guardian, but sometimes seeing the damage a cockerel/cock can cause to the feathers on the backs and heads of their girls can be troubling, and if you happen to have one aggressive toward people, difficult decisions have to be made, and children can be injured. I have three flocks with males and one pair of old ladies that live just with one another, and the old ladies' feathers are pristine. They still lay now and then, they eat grasshoppers in summer, and enjoy their peaceful lives.
I hope you enjoy keeping poultry as much as I do. I find they add immeasurably to our lives, doing their chicken things - there is little in the world I enjoy more than watching a chicken running full tilt after a grasshopper, without a more important care in the world at that moment.