Since the chicken tractor will be out in the yard, exposed to the elements, hardwood is your best bet.
Paint it with any water repelling stain with UV protection.
It will be heavy enough to deter strong winds and break-in attempts by determined predators. The caveat is that it can be really difficult to move it around.
As a workaround, look for tractors with large caster wheels that move freely on bumpy turf.
Hardware mesh is highly recommended on the run and on any windows in the coop.
If you are shopping on a limited budget, you can opt for chicken tractors made of PVC. But they tend to be really flimsy.