I agree with Michael.

Unmesh, material doesn't matter so much at very high frequencies. It's just to have it all, that helps.
There is special material arround which is otpimum: Thinned steel for HF-shielding purposes. I don't know exact name in english. Advantage compared with aluminium and copper is that it has additional screening effect due to big µr.
Essential for good shielding is to have big eddy currents. For this to have material's resisitivity must be as small as possible. For this reason only certain steel is good, assumed to have very much Fe. Certain thinned steel enclosure for HF-screening purposes is such very low resistivity material.
If you want to screen frequencies in GHz range any opening in enclosure must be as small as possible. You just should achieve completely surrounded Faraday cage.
If you cannot use thinned steel enclosure, I would take copper. Even single layer printed circuit board material can be used. It can be soldered directly on PCB massplane all over it's length and can therefore be advantegous even to superior material, which is bonded to massplane only at certain points. Disadvantage of rather thin (35µm) PCB copper plane is that at lower frequencies shielding is not so good compared to special thinned steel enclosure.

Bye,
Kai