I hadn't thought about Faraday Cages for a while, and was moved to google for information.
I work in an area with metal mesh inside the walls that was intended to block electromagnetic radiation. The mesh appears to be steel (certainly not copper or aluminum) diamonds roughly 1/4" wide, 1/2" tall, and 1/16" deep. The attenuation is enough to make my cell phone essentially inoperable, but others with (better) cell phones can make/take calls (but the reception is poor). It's also enough to effectively prevent the use of radio and TV.
My recollection on the theory behind Faraday cages is that electromagnetic radiation that trys to pass through a (perfectly-conducting) plane of material will induce eddy currents that offset the incoming waves, leaving a net of nothing on the opposite side of the material (and amounts to reflection of the incoming waves). There's no such thing as a perfect Faraday cage we can't use superconducting materials (at least not yet). This means that the induced eddy currents to not completely offset the incoming waves, and the net on the opposite side becomes some fraction of the incoming waves. So, the lower the resistance of the material; the more the incoming waves are attenuated. Therefore, look for lower resistivity and greater thickness to improve performance.
While a solid plane of material is best, cages made from mesh are common. I do remember that the size of the mesh is tied to the wavelength of the frequencies you want to attenuate. I found one reference (
here) that: "Faraday cages are usually designed so that the largest mesh openings have a diameter of 1/10 of the shortest wavelength."
Here's a couple of other links you might find interesting:
Holland Shielding
Security by Design
Good luck!