16 guage minimum is what I would be looking at.What gauge would keep them out?
The only sure method of keeping rats out is not to have food in the run to attract them. Yup, I know it isn't practical for many keepers but it works.
https://www.weld-mesh.com/welded-mesh/10011-galvanised-weld-mesh-1-2-x-1-2-16g-4ft-x-30m