I am now learning that chicken wire is not always the most secure from predators.
Chicken wire is good for keeping chickens in, but not so good at keeping predators out. Chicken wire is not very strong and many hungry predators can rip it apart without much problem. In your case, the coop is inside the barn, which does add some protection.
What predators do you have to worry about? If you have mink, weasels, or racoons, then I think you might need to upgrade that wire to 1/2 inch hardware cloth as already mentioned. If small animals like that are not your concern, maybe the chicken wire is good enough.
I know everyone will tell you 1/2 inch hardware cloth is the best, and it probably is, but it's also very expensive. If you are on a budget, then you end up weighing the cost/benefit of upgrading the wire in comparison to the chance of a predator attack.
I know I got to the point with my setup that I had to ask myself if I was willing to spend hundreds of dollars on 1/2 inch hardware cloth to protect my $30 investment in the chickens themselves, from an attack that may or may not ever happen. So I decided to use 2x4 welded wire and dog kennel panels which I already had for my chicken run, but built a Fort Knox coop to lock the chickens up at night. My setup is predator resistant, but not predator proof. IF I ever do suffer an attack, I'll reassess my defenses at that point.
You did not show a picture of your chicken run, but my concern there is if you have an automatic door, then you will be opening up the coop to any predators that may be in the chicken run. I don't have an automatic door, so I am forced to check the run each morning before I let my chickens out. At night, I have to look inside my coop to shut the pop door. So I am confident that no predators have hidden in the coop during the day. If you have an automatic door, then I think you would have to upgrade your run to be as predator proof as you can make it.
Looks like you will have a very nice setup for your chickens. I like the PVC feeders I see in the picture. If you have mice in the barn, you might be feeding them too - unless your chickens catch and eat the mice. Do you use the PVC pipes for water too? I have seen some people use PVC pipe with nipples for water and that seems to work well if you don't have to worry about freezing temps.
How do you collect your eggs? Could not see that in the picture.