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Copper foil (sometimes adhesive backed) is used as it is readily solderable, a (flexible) PCB substate is also often used as the geometry can be tailored by a standard process.
Aluminium and aluminum coatings on plastics are common if no soldering is needed.
Silver is common in radio frequency cavity filter plating to garner the best benefits of the skin effect at microwave frequencies.
Sheet steel is popular for sub-circuit covers and component cans as it is cheap and readily formable. Shapes are made with photo etching, die stamping and laser cutting.
Flexible elements are often made from woven or knitted meshes and sometimes small scale 'expanded metal' or perforated foil is to be found where reduced weight or freeform shape is required.
Surface coatings can be painted metal powder of zinc or silver. Thin coatings on plastic substrates would be more likely vapour deposited, sputtered or electroplated metals like aluminum, nickel, silver or gold.
All of these metals (except aluminium, nickel, silver and gold) will usually be coated with a less reactive metal, tin usually, for corrosion protection.
Lead and stainless steel are at the bottom of the list due to lower conductivity but given that a slightly thicker sheet could be used they are also an option if nothing else is available. They would more likely be selected due to their corrosion resistance and strength or flexibility.
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