What I understand you are wanting to do is build a movable run for a few chickens to be in during the day. At night you would lock them in a coop. That way they can get the green stuff, seeds, and creepy crawlies during the day and be safe in the coop at night. I could easily be wrong. I'll admit to being a little confused when you talk about hardware cloth on the upper part so they'd be protected from digging predators during the day.
For the movable run, I think your biggest risk during the day is probably dogs or hawks. Raccoons and foxes can be out during the day, usually just at dawn or dusk, so they are still a risk. I don't know the size you are planning for the movable run, especially how tall you are making it. I'd suggest hardware cloth for the sides since it is strong enough to keep dogs and raccoons from getting through it and the holes are small enough to keep raccoons from reaching through. You can use hardware cloth for the bottom two feet of the sides and use welded wire the rest of the way up. Or you can use welded wire (I'm thinking of the 2" x 4" welded wire) for the sides and line the bottom two feet of the sides with chicken wire or hardware cloth to keep the raccoons from reaching through.
For the top, I'd suggest either welded wire or hardware cloth. If it is tall enough a dog cannot jump on it, you might be OK with chicken wire, but a raccoon can climb up there and get through. I have seen a report on this forum where a hawk dove through chicken wire, probably did not see it. You could always weave ribbon or something through the chicken wire to make it visible to a hawk, but I'd suggest the welded wire. I'm thinking this run is not going to be too big since it is movable and you may have enough welded wire on the roll left over to do this.
I would not put wire on the bottom of the run. It will interfere with the chickens scratching and could hurt their feet. If the chickens are in the run when you are moving it, you really have a big chance of hurting their feet. I'd go with aprons to keep things from digging under. Aprons directly attached to the run could make it real hard to move the run, so, depending on size, I'd consider making some removable aprons. Maybe attach 18" to 24" of hardwire cloth or welded wire to a 2x4, put nails or lag bolts in the bottom member of the run side (assume 2"x4 bottom of the run) and leave them sticking up a bit, then drill holes in your apron to match the nails or lag bolts. Or what might be easier, drill holes in the 2x4 on the apron and the bottom member of the run and drop 5" nails in to act as pins.
I don't know how big a coop or what style you are talking about. They do like to scratch in the litter. You can bury welded wire under several inches of dirt, then cover that with litter, and they should be OK. It will eventually rust and you won't know when your protection has rusted away. Depending on the size, you can always make the floor solid wood. For my 8' x 12' coop, I put an apron of welded wire around it and feel pretty comfortable about anything digging in.
If I have misinterpretted what you are trying to do, please correct me.
Good luck!!!
