I agree with not using insulation. I live in Michigan and the winters get VERY cold...last winter we had many days in the low negatives with awful wind chill. My coop is not insulated at all. The hens each put out about 10 watts (if I recall correctly) of heat and huddle together on the roost. I've read that many breeds can deal with temps around negative 30 degrees. Also, I do not use a "heater" or bulb because then they won't develop the heavy feathering after molt to withstand the coming winter. I don't know anything about California heat, but I would assume if they have great ventilation and shade, they should be fine.
The coop looks great so far! Way to go!
I don't know what types of predators are common to your area or whether you are rural. Here, many of our predators won't venture real close to the house especially with all the neighbor dogs tied close by at various intervals. For my wire, I used the green-vinyl coated. Nothing can get through it (unless they run really really fast-lol, or can squeeze between the openings in the wire). A three foot tall, 50 foot roll cost me $32. Around the lower perimeter of it, I stapled chicken wire over it (about 2 feet up) just so that when I have younger or smaller hens, they can't "walk through" the openings. I lost two young Guinea Keets that way last year, lol. (If you're not sure of the green wire option I'm talking about, there is a pic on my member page of my first try at building a coop).
Have you decided on roof materials? Personally, I like the flexibility, water-proofing-ability and the look of shingles. With only needing a few to cover, it won't be very heavy and will match your house better. Also, things like steel can cause some major owies when trying to nail it on or even just moving it around or cutting it.
I see there is a close fence on one side and then your house next to it. Will there be adequate ventilation and air movement? It is hard to tell looking at pics. Just a thought.
I meant to add, I also agree that chicken wire is really only good for keeping chickens confined. It rusts and breaks easily, and pretty much anything can get through it to the chickens.