A faraday cage is a pretty simple device. You take a conductive material and make a box out of it, then ground it. Because the material is conductive, when an electromagnetic wave hits the box it is transmitted to the ground and fails to pass through. The box can be completely solid, or made of a mesh (with the mesh, you need to calculate the size of the holes in the mesh to determine which frequencies will pass through and which will be caught).
The thickness of faraday cage materials just needs to be thick enough to carry your EM wave to ground. A piece of aluminum foil is more than thick enough to block out most high frequency waves that are going to be floating around in the air in your home. If you want to block out very powerful low frequency waves, then thicker will work better. 1/8th of an inch thick seems like ridiculous overkill . . . a 1/8th inch copper wire is 8 AWG and can easily handle 40-50 amps of electricity at a couple thousand volts. If you have anywhere near that amount of EM power going through the air, you're probably not going to worry about interference with your guitar because you'll be dead.