I've been trying to find good English-language sources on this topic myself, and unfortunately I haven't turned up any that are specifically about military organization- only general histories that touch on military topics. Even contemporary military treatises tend to focus on top-level strategy and not on the practical details of tactics, equipment, organization or logistics. But the good news is that military developments went hand-in-hand with social and political developments, so their general character can be traced even if the nuts and bolts sometimes can't be.

Looking at your timeframe (~400BCE-200CE), we can best break it down in thirds. Roughly 400-200BCE covers the Warring States up to the Qin unification in 221BCE. Roughly the next two centuries covers the imperial Han army until the end of conscription in 31CE. The last two centuries will cover the new professional/mercenary army until the breakdown of Han authority and the Three Kingdoms period, when the last Han emperor abdicated the throne to the first Wei emperor in 220CE.

The Warring States effectively saw the destruction of China's old aristocracy and their fief-oriented social organization, and the growth of something more like absolute monarchy with a national draft. Prior to the 5th century BCE, Zhou armies were made up of chariot-riding aristocrats and their armed retainers, organized on the basis of lineage- warfare was reserved for the highborn. But from the 5th century on progressive technological and political changes, plus steady attrition due to escalating warfare, broke that model down. For one, the spread of ironworking and the invention of crossbows and lamellar armor made infantry both more effective in combat and less expensive to arm; two, newly-rising southern states- Wu, Yue, and to a lesser extent Chu- had no charioteering tradition and therefore were eager adopters of new and better infantry-based techniques, pressuring the central states to adapt in turn; three, in order to cope with rapid territorial expansion, states were getting better at registering and tracking their lands and people, making it possible to implement mass mobilizations. Monarchs were taking advantage of these same territorial changes to put more land under the control of centrally-appointed administrators rather than hereditary noblemen, which further strengthened central authority and caused the aristocracy to wither.

The overall impact of these changes was to shatter the old superstructure of landed, elite collateral lineages and bring the individual commoner and the central state into direct contact with each other. The remnants of the noble lineages, now dispossessed of their independent powerbases, became shi, "men of service" who filled the growing military and administrative bureaucracies and lived off of state salaries instead of peasant rents. Peasants increasingly held their own land but owed military service in addition to taxes and labor. Military ranks, formal unit sizes, and training drills were all implemented, though in different forms by different states. The sources I have on hand indicate that a year of military training would be typical for conscripts, although it could be more intense for elite troops like the corps of horse archers established in Zhao in 307BCE. As part of their Legalist reforms in the mid-4th century BCE, the state of Qin went the furthest by sorting the entire adult male population into ranks- rank was gained mainly through taking heads on the battlefield and was rewarded through land grants and tax favors. By the time of the "Seven Hero States" the typical Chinese army would be a mass of conscripted infantrymen armed primarily with crossbows and polearms, unarmored or wearing leather lamellar, having undergone some degree of formal training, divided into units of uniform size and under the command of a hierarchy of officers and supported by more elite units (whether drawn from royal guards, special standing formations, or designated military households) which could be cavalry, charioteers or more heavily-armored infantry, all under the command of generals appointed directly by the monarch. Visually the terracotta warriors are very good representatives of what one of the better Warring States-era formations would have looked like.

The early (Western) Han military experience can be seen as a gradual shift away from fighting other Chinese and towards fighting the Xiongnu. In the 3rd century BCE, the Xiongnu confederation emerged as a steppe empire powerful enough to threaten a unified China, and the military model inherited from the Warring States was utterly ineffective at resisting it. After a particularly crushing defeat at the hands of the Xiongnu, the Han state essentially became their tributary for a period of roughly fifty years. During this time the conscript infantry still found use in internal conflicts as the Han emperors gradually broke up their vassal kingdoms, and in manning the empire's border defenses. The reign of Emperor Wu (140-87BCE) marked the turning point, as the now-consolidated Han state built a cavalry army capable of fighting the Xiongnu on even terms. This army was necessarily smaller and better-trained, and called for extended periods of service. Fortunately, economic expansion and massive minting of coins meant that the Han state was by then able to collect cash payments in lieu of the military draft and could use those funds to provide for career soldiers. These professional soldiers made up the mounted field armies that could take the fight to the Xiongnu as well as the infantry garrisons who could permanently occupy strongpoints along the frontier- they were also bolstered by convicts and by nomad mercenaries. This new army eventually broke the Xiongnu confederation, and after the Wang Mang and Chimei crisis, conscription was abolished altogether in 31 CE.

Over the next two centuries, up to the end of the Han, this professional army was increasingly supplemented by nomadic allies under a system that closely parallels the Roman foederati. Large numbers of nomads, organized into various tribes, were settled within Han borders in the frontier regions and were allowed to keep their own leaders, under the supervision of Han garrisons. Increasingly the Han state gave up on raising their own horses and training their own soldiers as cavalry, outsourcing these tasks to nomadic allies and filling out the numerous border forts, watchtowers and frontier towns with Chinese infantrymen. Meanwhile in China proper, a class of major landowning families was emerging, using their educational advantages and social networks to monopolize office-holding. When the Yellow Turban revolts broke out across China in the 2nd century CE, it was these powerful landlords who equipped and organized their retainers as private armies, or buqu, to suppress the regional uprisings. Later they used these private troops to destroy Dong Zhuo and the northwestern army under his command, ushering in the collapse of the Han and the beginning of the Three Kingdoms.

References:

Early China: A Social and Cultural History by Li Feng, Cambridge University Press

The Early Chinese Empires: Qin and Han by Mark Edward Lewis, Harvard University Press

East Asia: A Cultural, Social and Political History by Ebrey, Walthall and Palais, Houghton Mifflin