I am a big fan of the "Dandelion Dynasty" series of silkpunk fantasy novels by Ken Liu. I recently learned that the first book, The Grace of Kings, is apparently a nearly beat-for-beat retelling of the Chu-Han Contention. As historical fiction, the book would be excellent, but of course some elements are fantastical and unreal. I feel like I managed to learn a lot of ancient Chinese history without realizing it, but now I would like to know what is based in real history and what is not. Sadly, my education was slanted heavily Eurocentric and so I am pretty ignorant of Chinese history.
How can I learn more? Are there books (straight history or historical fiction) that are accessible to a complete beginner? Any suggestions are most appreciated (and I hope this question is properly formatted for the rules of this sub)
Unfortunately, compared with later periods, it's hard to find accessible English-language monographs covering this important era in imperial Chinese history. The Cambridge History of China, Volume 1 (Chin and Han) is a good starting point, but it's not inexpensive and not available as an e-book. The same goes for Michael Loewe's Biographical Dictionary of the Qin, Han, and Xin Dynasties.
Another excellent option is the closest thing to an "original text" that we have - Sima Qian's Records of the Grand Historian, written during the Han dynasty and covering the Chu-Han contention and its participants in great detail. Sima Qian was a Han dynasty historian who essentially founded traditional Chinese historiography, and his writings on this era will serve as the basis for just about any contemporary or near-contemporary monograph on the subject. These are nicely translated into English, highly readable, and very engaging, although the historical narrative is organized and structured very differently than a modern narrative history.
If your interest in ancient Chinese history is broader and extends to civil conflict beyond the Chu-Han contention, there are more options available focused on two comparable periods of unrest during and after the Han: the restoration civil war of the first century, and the Three Kingdoms period of disunity. There are lots of great resources on these eras available online (Hans Bielenstein's highly engaging works on the former are available for free online), and anything by Rafe de Crespigny will give you a good overview of the latter era).
I don't want to break any sub rules by offering too much in the way of historical fiction recommendations, but if you'd like to "illustrate" your readings on the Chu-Han era, the historical drama King's War (available on Netflix) is a pretty fact-faithful rendition of the era as related to us by history.