Bronze is an alloy of Copper/Arsenic or Copper/Tin. The use of pure Copper began before the Age of Bronze or Iron. This is probably because:
Copper can be found in it’s pure state naturally (although this is rare)
Copper ores are an attractive Blue/Green color and were used to decorate/pigment pottery that was then fired in a furnace. Firing copper ore in a reductive charcoal pottery furnace at high temp would have lead to the discovery of Copper smelting (producing pure Copper metal from it’s ore).
Copper itself is an attractive red/gold metal that was sought after for ornaments and jewelry. It also served as a good material for some tools.
The discovery of Bronze (Copper/Arsenic and Copper/Tin alloys) probably occurred by accidental contamination in the smelting process, since copper ore is found in areas that also contain Arsenic and/or Tin ores. Bronze is a harder metal than pure Copper and thus can be used to make tools that have a sharp edge: (axes, knives, swords etc.)
Iron smelting, uses a process nearly identical to Copper and Tin smelting and Iron metal was being produced during the Bronze Age. Although Iron is much more abundant than Copper or Tin, it was not favored for weapons and tools because:
The relatively pure Iron (which would now be called Wrought Iron) produced by the early smelters was softer than Bronze and didn’t work as well for edged weapons or tools.
Iron is more reactive chemically and would rust much easier than Bronze. It required a lot of maintenance to keep Iron tools from rusting.
Often officers would have the bronze swords and the common soldiers would get the cheaper softer Iron swords.
However the Tin ore used to produce Bronze is not very common and eventually known Tin resources became exhausted. This led to the widespread use of Iron. Eventually is was discovered that alloying Iron with Carbon produced a metal harder than Bronze and the Iron Age began in earnest.