My uncertainty is a function of your ambiguous questions. You've not stated anything about purpose, dimensions, frequencies, field levels.
Magnetic shielding is a function of thickness and permeability. Fully annealed, low carbon steels have the highest permeability. If you want greater permeability you need mu metal which is almost pure nickel and very expensive. The thickness required varies with frequency. The permeability also changes when the metal is deformed, so annealing is required for best performance.
Electric shielding is a function of conductivity. Here also the thickness required varies with frequency, but not so much as the magnetic case. Copper is certainly more effective than galvanized steel, but it is a lot more expensive. Silver is better than copper. For a small enclosure the cost is nominal, but for a room it's too expensive even for commercial shielded rooms. Copper screen is effective at low frequencies, but loses effectiveness as the wavelength approaches the mesh openings.
It should be noted that a superconductor provides perfect electric and magnetic shielding.
There is a lot of information on the subject in this:
https://www.amazon.com/Electromagnetic-Compatibility-Engineering-Henry-Ott/dp/0470189304I suggest reading it.
In particular there is a lot of experimental data presented about the effectiveness of different materials and thicknesses.
There is no single answer. It depends upon what you are trying to do. And the shielding material quickly becomes less important than how the seams and penetrations are handled.
I am very sure about what I am doing. I'm using 26 gauge galvanized steel sheet as sold to the HVAC trade. It is the cheapest material, provides decent shielding of both the electric and magnetic field above a few MHz and is easily soldered to seal the seams. IIRC a 12' x 16' x 8' room will run about $1200-1500 for the steel. Copper screen would be 2-3x that and copper sheet probably 5-6x.
Reg