1/2" or 1/4", it still comes in different gauges. Always get the heaviest one you can find.
Meanwhile, what the OP used looked substantial to me so I wouldn't worry him on that account.
I think it's a very nice start but I have to echo some of the concern about predators and rodents.
Do I see voids along the top of the run that rodents could crawl through? I'd be worried that a small determined raccoon could get through there too. Their skeltons are far smaller than their...