Like most Chinese dynasties, the emperor was in control of the entire government, and outranked everyone else.
Liu Bang: The Han dynasty's emperor.
"During the reign of Emperor Wu, Liu Che who ruled from 141 - 87 BC, the Han Dynasty Porcelain Jugs of Western Han Dynasty Porcelain Jugs of Western Han Dynasty achieved its most powerful and prosperous period" (Travel guide China)
The Han dynasty was one of the first unified, Chinese dynasties. The first emperor, Liu Bang, Emperor Gaozu initiated many effective measures by recruiting people for his government based on their ability, not birth or wealth, and drawing lessons from the collapse of the Qin and former dynasties. The economy recovered very quickly with able people in the government and with policies based on Lui Bang's reforms. The arts were encouraged by Gaozu and flourished. After Gaozu's death, his son Liu Ying succeeded to the throne although power was held by his mother Queen Lv Zhi. After 16 years of reign by Lv Zhi, Liu Heng (Emperor Wen) and Liu Qi (Emperor Jing) became the emperors in succession. They both reduced the people's tax burdens as Emperor Gaozu had done and encouraged the people to farm and be thrifty in life. Due to their effective measures, the people lived in stability and the nation's wealth and power were enhanced greatly. So far politics are at the bottom of the list due to it's lack of difference, when comparing other dynasties since each dynasty, Qin to Ming has a single ruler, known as the emperor.
Chinese coins, used as ancient China's currency
"The Han dynasty (206 BC – 220 AD) of ancient China experienced contrasting periods of economic prosperity and decline. ... The Han economy was defined by significant population growth, increasing urbanization, unprecedented growth of industry and trade, and government experimentation with nationalization". (Wikipedia)
In agriculture, water conservation and irrigation projects were built and greatly expanded production. Cattle, and iron farm tools were used at large to plough the land, and planting skills were also improved greatly, thus helping the economy. My ranking of this would be bellow government because like many Chinese civilizations, and ancient civilizations in general, agriculture wasn't an innovation created by China.
"The Han dynasty is oftentimes regarded as one of the most successful of all the Chinese dynasties. The practices and traditions during this dynasty helped set the tone for the imperial rule that governed China for over 2000 years. Like all the other dynasties, religion played a great role in shaping the rule of those in power" (Totally History).
The religious legacy of the 400 year Han era was the development of Confucianism and Daoism, and the acceptance of Mahayana Buddhism. During the Western Han era, the religion of Daoism developed that became China's major indigenous religion.