What would be a good book to learn more about ancient Japan?
There really isn't much to go on. The 3rd Century CE Chinese text The Records of Wei 魏志 is the only substantive historical document talks about Japan. In it, a Wei kingdom scribe and possibly diplomat travels to the islands of Japan, to at least eight distinct locations and describes what he finds. The climax of his journey is the arrival in a large city of 70,000 households, ruled by a female ruler. There are many basic descriptions in the text of the cities, but nothing terribly specific. For a nice translation and extensive notes, see J. Edward Kidder's Himiko and Japan's Elusive Chiefdom of Yamatai: Archaeology, History, and Mythology
Outside of the Wei Zhi, there is archeology - most of which focuses on the great Kofun mounds, pictured here, as you can see, they are BIG. There is much to be learned from these mounds and archeological exploration of the period, but historically, as I said, Wei zhi is it.
What do you mean? Religiously?