I would do a solid roof too- and as others have mentioned- make sure every member of your family can stand up in the run. When it comes time to clean - and it will - not having to hunch over is a huge plus.
Also - if you do decide to only do a solid roof for part/all of it- I would ensure that the area near the pop door is under it. If you live somewhere very wet- keeping your ramp and the pop door area relatively dry will help keep chicken feet dry which will in turn make for cleaner eggs in the wet season.
Even if you're in a dry climate- the permanent shade afforded by a solid roof can make all the difference when it comes down to keeping the chickens cool. Having extra shade by the pop door can also help the coop stay cooler.
I would use shade cloth (like Coolaroo (or whatever)) on the FENCE - i.e. the south and west sides of the run, not over the top -- so when the solid roof isn't providing any shade because of the angle of the sun in late afternoon- the shade cloth
still provides relief. I would leave the first 2 feet up from the ground open for maximum air flow at chicken level.
Money and labor spent now is easier than working in a hurry to make up for a deficiency!
Also - depending on predators in your area- you may want to look at electrifying the area around your solid roof.
And while I know this isn't the topic - use hardware cloth EVERYWHERE on your run fence- never chicken wire-- that won't do anything but keep the chickens in. Dogs, raccoons, cats, hawks - defeat it easily. Hardware cloth is the gold standard. This article shows the fence a hawk reached through and killed a bird.
http://www.the-chicken-chick.com/coop-security-hardware-cloth-vs-chicken/
The shade cloth wouldn't be a substitute for hardware cloth, of course.
If you're going to have hens with baby chicks- or baby chicks- do hardware cloth top to bottom. Chicks can slip through the smallest openings. And even if all they have to do is slip back in the same way they came- they almost never do. Then you have the distress calls to mom that attract anything looking for a meal...
Also - remember chicks can fly. That's the reason I say hardware cloth top to bottom (check
Amazon for the best prices- much better than local stores, farm or otherwise) is chicks will fly up to perch on little spots- like say the hole area of a chain link fence. Then they jump through and we're back to a panicked chick.
Even if you're fencing with something like chain link or no-climb horse fence- and will be keeping only adults - remember - the chickens can STILL stick their heads through the openings to get whatever is "greener" on the other side- which makes them vulnerable to animals who can reach through those same holes, or just flat grab them by the head/neck. Have hardware cloth high enough up that none of your birds can stick body parts out- I would go 3 feet up and if you can, 1 foot down into the ground with it.
