How much you prepare for predators depends on your local predators. In my case the young chicks who got out of the chicken run were killed by our own family doggies (schnauzer/poodle mix = schnoodles). So we had to reinforce the run to keep the chicks IN, as the run was already enough to keep the dogs OUT. We built the inital run with 16' long by 5' high Tractor Supply Horse panels. It has 2"x4" gaps. Not enough for a full size chicken to pass through, but we found out the chicks pop through like it isn't even there.
www.tractorsupply.com/en/store/horse-fence-panel-5-ft-x-16-ft
We added something similar to this but in plastic (cheaper). This would keep the chicks secure inside (excepting for gaps under or around the ends of the wire).
www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=Welded%20Wire%201%22x1%2F2%22
I came home today and was very surprised to see about 8 of my full size birds had either flown over the run fence or wriggled through the gap I must have left at the gate. I'd let the dogs out and heard chicken commotion and went to see what was going on. The chickens were nervous with my dogs running loose, but the dogs hardly seemed interested in the full size chickens. I think my dogs are primarily interested in the chicks which are the same size as their doggie squeeky chew toys. Don't those little chick cheeps sound just like a chew toy squeek?!
I tend to overbuild in general (such as using horse panels for a chicken run), but if you'll have small day/week old chicks running about I'd recommend 1/2"x1/2" mesh or no larger than 1/2" x 1" hardware cloth to keep the chicks where you want them until they're too big to fit through any larger gaps. For me, it seemed about 4 weeks of age before they couldn't fit through the 2"x4" holes in the panels.