Although the western world was fairly comfortably in the Bronze Age in many places by 2000 BC, it makes sense to start out in a Stone Age. This doesn't mean cave man, however, simply a culture that doesn't work metals. There are many examples of very culturally advanced stone age cultures, such as the native Americans, especially those of central and South America. These cultures are still perfectly capable of advanced mathematics, construction, and warfare. You can also have this be an age prior to the domestication of animals.
Starting in 2000 BC, you are in the Bronze Age. There is limited metal working, and the material of choice for weapon implements in bronze. Being softer than other metals, it favors shorter blades and points, so lots of short swords and spears. Generally, your bronze age cultures are practicing animal husbandry and domestication, so you start to see a lot of animal influence in military and agriculture.
The next good point is the Classical Age. At this point in time, many cultures had started working in iron and lead. This was the age of the ancient empires, when huge swaths of territory were coming under centralized control. With the influx of resources and growth of population, art and culture flourished in this, one of the first times in human history in which a great deal of recreation time was available for some classes of people. This is also where you begin to see a popular proliferation of planned cities, and massive, large scale domestication and deforestation.
From the classical age, you find yourself in the Iron Age. Finally, metallurgy is really starting to dominate production. True machines, albeit primitive ones, are able to make use of stronger materials to be durable enough for long-term function. Gunpowder first appears in this age, but it is used in little more than primitive explosives. Still deadly, but it hasn't been refined or fully exploited for its potential.
The Iron Age leads to the Feudal Age. The massive proliferation of weapons technology and increasingly scarce resources has come to favor smaller kingdoms over the larger empires. Each small territory has to hold its own defenses and armies. Complex systems of loyalties and laws tie larger areas together into loose confederations for trade and defense. Technology remains relatively stagnant, but the true shape of modern borders is being settled in battles and negotiations.
After the Feudal Age, I think the next good period is the Age of Exploration. With the world fairly well mapped and populated, long-distance trade and travel becomes lucrative, especially as resources dwindle in the places that have been continuously populated for over two thousand years. Economics grows into a complex powerhouse, fueling a proliferation of smaller, more private military outfits to compliment and serve the rising oligarchy. Central authorities are beginning to have to make concessions and share power. You see development in the fields of transportation, optics, astronomy, and a massive exchange of culture and ideas. Gunpowder technology has truly grown. You have cannons, hand-cannons, and the blunderbusses. The old type of heavy plate armor is absolute in the age where any regular recruit can potentially shatter your defenses, and battle favors mobility more than ever.
Then you enter your Golden Age, the time when higher thinking and higher learning is beginning to make the old systems of governance obsolete. Complexity is ever-increasing, and war has followed suit. Gunpowder technologies have been perfected into effective, accurate and deadly forms. Still primitive, by our modern standards, but perfectly good weapons.
