I live near your area, a little south of Tacoma so we get the same weather. You definitely need something besides just wood for your coop roof! I agree with metal roof panels - but if you want to save $$ polycarbonate or PVC roof panels will work.
I used green PVC panels, they were I think $16 each from Lowe's. Maybe they won't last as long as metal, but so far so good. My coop is in a sheltered area under some trees, so they don't get as much UV deterioration than if they were under constant sun and rain. They are 8 feet long and my coop is 7x12, so I got a 1' overhang on the high side, and the low side I made flush to direct the rain into a gutter and then to a water barrel.
You do have some other options for the run besides total hardware cloth - my run is 18' x 25' six foot tall around the sides and taller in the middle. What I did was first build the wood frame, then cover everything (including the roof) with poultry wire that we had lying around, so I'm not sure of the price. Then I bought a roll of 100' long by 4' tall hardware cloth from
amazon for I think $148...this was a few years ago so it might be more now. And two 50' rolls of 4' tall welded wire for pretty cheap, like $40 for both.
I used the hardware cloth along the bottom of the run, going up about 30" then bent it to form an apron extending outwards along the ground about 18". Above the hardware cloth, I installed the welded wire up to the boards along the top. And attached the top of the hardware cloth to the bottom of the welded wire by "sewing" some plain wire.
Here are some pictures:
The coop (chain-link dog kennel, covered sides and top with poultry wire, hardware cloth apron) with PVC roofing, gutter to rain barrel, small house inside.
Wire and hardware cloth attached to posts, upper and lower framing with screws and washers
The hardware cloth keeps out all predators (unless you have bears!) and pests like raccoons or coyotes can't get through the welded wire, and with the layer of poultry wire inside the welded wire, smaller pest like weasels and rats can't get in. The poultry wire on the roof keeps hawks and owls from swooping down to grab the chickens.
We're really happy with this run, nothing has gotten in, even though we have raccoons, we've seen coyotes in our area, and one time I scared off an owl who was sitting on top, trying to figure out a way in. And it was way less expensive than doing the whole thing completely in hardware cloth.
We still have more improvements to make - our current coop is roofed with a small house inside it that has roosts and nest boxes, but as you can see from the first picture, the sides are just wire that we cover with plastic when the weather is freezing. We are working on converting the old horse trailer you can see next to the run, to make it our main coop. Then the current less-sheltered coop will be for raising meat birds maybe, or just an alternate coop if we need to quarantine some chickens, or separate a broody and babies.
If you're in Seattle city or suburbs, you probably have a smaller flock than we do, and could do something like this on a smaller scale relatively inexpensively. Make sure you don't skimp on screws and washers, though! It really is the most secure way to attach any kind of wire to wood, that pesky raccoons can't pull out like they can do to staples.
I despise wood due to mites here in the southeast. Ive used clear panels in the past from lowes that suppose to be UV protected.. they deteriated within a few years and started cracking. If you use clear or tinted panels get a high quality one and I would only do a couple of them for light and use metal on the rest, my friend did that on his barn, 1 clear panel for each chicken pen inside and it lit up the rooms really well
