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Sorry, I thought I *was* specific -- I would suggest using 2x4 welded wire, no less than 4' tall and preferably taller. Buy as much as you can for your $125 and then that's the size run you have -- reduce number of chickens if necessary to fit gracefully. Then spend $25 on a roll of plastic 1/2" garden mesh (it is pretty flimsy) and add that to the bottom 2'.
Or find something secondhand, which would be cheaper but requires work and patience.
To digproof (more or less) on a budget, get a bunch of large (hard to lift) rocks, or (better yet) sharp concrete rubble in largeish pieces, and half-bury that in an 18" wide strip all around the outside of the run. Not much will try to dig through that, if you get it really well set into the ground, and lots of people are happy to have you haul away their concrete rubble for free.
Good luck, have fun,
Pat