Copper conducts better and is generally used in higher-performance/modified engines. In dedicated race cards resistor-less copper plugs are used.
Iridium and platinum plugs are chosen for their longevity only. You shouldn't gap iridiums because of potential damage to the tips. For that reason and their inferior conductivity, they aren't used in modified engines. Keep in mind their price, as well.
Any claims of more power or fuel efficiency of one type over another are pretty much baseless unless you were using the wrong plugs to begin with. Stick with what your owner's manual calls for unless you have a reason to upgrade/modify. For example, if you have a turbocharged car but are running more boost you might gap your plugs a little smaller to accommodate. The claims by parts stores to upgrade to the Triple-Spark Ultimate Unobtainium plugs are just upsells.