Plastic "hardwarecloth" is NOT AT ALL predatorproof. It will keep your chickens in, but it won't keep hungry predators out.
IMO the best compromise between budget and security (unless you happen into a scrounged or discounted supply of something even better, of course) is to use heavy livestock-gauge 2x4 wire for the run fence, and add something smaller meshed on the bottom 2-3' (ideally hardwarecloth, but 1/2" chickenwire is very good too, and even normal 1" chickenwire or plastic mesh is really not *so* dangerous since all you're doing is preventing reach-through) and then make real sure to close the chickens into the henhouse every night by dusk.
Rats and weasels can go thru 2x4 wire, but they can go thru pretty much ANYthing frankly (they will find gaps) and weasels are almost completely nocturnal; baby raccoons and baby possums can go thru 2x4 wire too, but they are almost completely nocturnal. The actual risk of this construction is apparently small (you don't hear about people having problems iwth it) and it is certainly more affordable than all-hardwarecloth.
Pat