In case I didn't say it earlier, that's a great coop! Your husband did a nice job on it.
If you are going to keep the chickens locked up in the coop at night, make sure the window and vent openings are covered in 1/2" hardware cloth. This keeps out weasels, some species are quite small, rats and keeps raccoons from either getting in or reaching through and pulling your chickens apart. Gruesome, but another thing that has happened to people's chickens. Honestly, once you get the housing done, the rest is pretty fun. You just have to deal with the predator issues up front.
For a daytime run, I would still want something stronger than chicken wire. Unless you have a livestock guardian dog on patrol. All you need is one stray dog to really ruin your day. Sometimes, it's a neighbor's dog or even the owner's own dog. Even if you have a good fence, sometimes gates get left open. That's happened to people, too. Or a dog dug underneath.
I know some people layer chicken wire with welded wire over it. I haven't read of any losses from people doing that so far on this forum, so I think that's an option. For a small coop and run, you probably just need to figure out what the cost would be to buy both types to layer, compared to just the hardware cloth. Also, if you're going to put hardware cloth over the windows and vents of the coop, you'd have some of that roll left, anyway. I'd just look at those numbers and see what you think after that. As an example, you might be looking at 1 roll of hardware cloth, 1 roll of chicken wire and 1 roll of welded wire, compared to 2 rolls of hardware cloth.
For the person with only chicken wire over the top of their run, I would definitely add welded wire on top of that if you need to keep raccoons out at night. They definitely have been known to climb up and go through any gaps or flimsy covering. If it's just to keep out hawks during the day, chicken wire works great.