Firstly, the People's Republic of China actually encompasses the homelands of the traditional "Chinese" ethnic groups, as well as a number of smaller ethnic groups mostly, but not exclusively, on its periphery. This page addresses the Chinese heartland, that is, China minus Xinjiang, Manchuria, Inner Mongolia, and the region south of the Yangtze. Han Chinese were the dominant group in this region for a millennium or two prior to when the exercise starts. From the south, China was protected by geographic barriers, however for most of its history it has been menaced by the nomadic peoples of Central Eurasia. Specifically:
At the beginning of the study period, Northern China was the center of the Han Dynasty, an expansionist empire run from the ancestral homeland of the ethnic "Han" Chinese. Note that at this age, the ethnic Chinese were concentrated in the the northeast of their realm, roughly between modern Xian, Beijing, and Shanghai. The rest, including the entire southern half of the Empire, was not ethnically Chinese.
Third and fourth Centuries: Invasions and settlement of the Hsiongnu (Huns, maybe?) out of Mongolia into northernmost China. Even when the two nations were at peace, the Chinese allowed Hsiongnu to settle in northern China. This culminated in the Fourth Century with the invasion of a Hsiongnu group called the Toba. At this time, China was divided into three kingdoms. The northern kingdom was overthrown by the Toba, who founded the Wei Dynasty. (The Toba, incidentally introduced Buddhism into China). Thus, if your ancestors were in northern China in CE 500, they probably had ancestors in Mongolia and adjacent parts of central Eurasia in CE 1.
Sixth Century: Immigration of the Turks. The Turks emerged as a nation on the plains of Central Asia and Mongolia during the early sixth century. Soon, their offshoots had settled heavily in Xinjiang and served in the Chinese army. In fact, the mother of Tang Tai-Tzung, the founder of the powerful Tang dynasty (CE 617) was Turkic. Seeking to control them, the Chinese conquered and ruled their Central Asian homeland. A small Chinese aristocracy ruled there for over a century. If your ancestors lived in China in CE 1000, their ancestors might have lived both there and in the homelands of the Turks - Mongolia, Central Asia, and Xinjiang in CE 500.
1125: The pattern repeats. This time, the Jurchen (later called the Manchus) of Manchuria attacked and overran northeastern China. The Jurchen rulers called themselves the Jin Dynasty. if your ancestors were in Northeastern China in CE 1490, their ancestors probably also lived in Manchuria in 1000.
The thirteenth century: The Mongols conquered and controlled Northern China and gradually incorporated South China into the Mongol Empire. In 1259 Kublai Khan ascended the Mongol throne and moved its capital to Beijing. This city was the focus of the Mongols and their multinational administrative corps (Iranians, Turks, Arabs, a handful of Europeans like Marco Polo), was truly cosmopolitan, and developed an excellent communications system. If your ancestors were in North China in CE 1490, it is likely that at least a few of their ancestors could have originated anywhere in the Mongol Empire in CE 1000.
The seventeenth century: The Manchus conquered all of China and Mongolia. In China, they formed a new aristocratic class, the Qing Dynasty, which governed into the 20th century. Ironically this was the beginning of the end for the Manchu nation, as they were spread very thin governing a large empire and were genetically swamped by the ethnic Chinese whom they governed. At this time, the Manchu language is spoken only by a handful of elderly people. Thus, if your ancestors lived in Northern China in 1900 or 1800, their ancestors could have been in Manchuria in earlier periods.