If you're talking Zhou/Qin/Han China as ancient China, then actually Buddhism and religious Daoism (as we later know it) would be anachronistic for the time period. Those two religious primarily came into popularity during the post-Han Six Dynasties period.
Also Confucianism isn't really a religion, it's more of a hierarchical governing/life philosophy that extends from the ruler on down. Although Daoism and Buddhism also have their governing life philosophies, Confucianism also doesn't deal with the supernatural as much or in quite the same way as the other two, as it's primarily concerned with practical action in governing the physical world. It's more about the logic of the belief system than it is about the faith in the supernatural underpinnings of the belief system.
So with that said, the religion of Zhou/Qin/Han can be categorized as simply "ancestor worship." You offered sacrifices to your ancestors and honored kin in order to both relieve their suffering in the afterlife and hope they may intercede positively in your current life. Especially in Qin/Han times, the afterlife was not that much different from the current life. It also involved a vast bureaucracy that managed the affairs of its denizens. It also required the same amenities as the world of the living, thus why there are always replicas of houses and luxuries being buried in tombs along with the dead. Thus the world of the dead was quite intermeshed with the world of the living in ancient China (though this would change to be more separated as time moved forward), and the fear of the crossing over of the world of the dead into the living was an ever present source of anxiety, which is why elaborate replica tombs were built to begin with, to keep the dead in luxury so they wouldn't bother the living.
A second layer of religion were the state cults involving the emperor. Now this gets more interesting because here they didn't just worship their ancestors, but also the natural world. "Son of Heaven" wasn't just an aspirational title. It was as much a reflection of the worship of the physical sky/heavens as it was a worship of it as a separate realm of spirits. This same applied for worship toward the cardinal directions as Gods (north/south/east/west). Something interesting to think of, not only is HuangDi a definition for emperor, but it's also a connotation for "central cardinal point" (directions had colors associated with them, green for east, red for south, yellow for center, etc.), thus simultaneously connotating the emperor as a god of this "central kingdom" which is what the Chinese call China, ZhongGuo/Middle Kingdom.
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