This answer is based on History Of Metallurgy (historyworld.net) and Wikipedia page on metallurgy history.
The first metals man was able to work with, were probably gold and silver due to their very low reactivity rates and high chances to find a pure gold or silver block. However, while these metals were aesthetic for the ancient peoples, they were too malleable to be put to use in objects where brittleness was required. You could easily make a usable drinking glass with gold or silver, but a pure gold knife would be useful only for cutting soft fruits.
The next metal people came across was copper. The metallic age began with rising use of copper by circa 7000 BC. Copper is less reactive than iron and melts at lesser temperature. This means that if/when the ancient peoples accidentally placed a mineral stone rich in copper in their camp fire, they ended up with pure copper lump in the morning. Heating and molding gold had already taught them how to melt these strange minerals and once they found copper tipped weapons useful in combat/hunting, copper age was on the way.
Another form of getting metallic objects was scavenging for meteorites after a shooting star crashed down in the vicinity. Meteorites are known to contain a high content of metal (specially iron) and relatively low on rock (silica). The people incorporating such pieces of meteorites would have found them to be extremely useful when used for cutting or stabbing.
Serbs were already smelting (heating ores in fire to melt the metal and obtain it in pure form) ores by 6000 BC. There are signs of copper smelting in southeastern Europe by 5500 BC. By 3500 BC, smelting was common around most parts of Europe.
The idea of alloys was in swing by 3000 BC. The first alloy to be prepared was bronze (copper and tin). Alloying technique originated in prehistoric Iraq and gradually spread to south Asia before becoming widespread and reaching Europe by 2000 BC.
The next and by far the most important metal was iron. Iron ore is harder to purify than copper or tin and requires complex processing. This is why iron mining and purification signs are found no sooner than 1300 years BC.
People were introduced to metal through pure lumps of gold and silver.
Copper, tin and lead containing stones were found to be refined easily by simply putting them in fire.
Iron containing meteorites were highly prized for their brittleness and strength.
Copper age began around 7000 BC. Alloying became a norm in around 3000 BC and iron mining was in place by 1200 BC.
So then, if you ask what metal people discovered before others, it would be gold. If the question is, which metal started the metal ages, it was copper, followed by tin, lead and finally iron.