Reddit mentions of Chinese Civilization: A Sourcebook, 2nd Ed

Chinese Civilization: A Sourcebook by Patricia Buckley Ebrey

A very easy read with ancient texts from different periods of Chinese history

I think the work of Patricia Ebrey is perfect for what you are after. Try these books:

China: A Cultural, Social, and Political History
and
Chinese Civilization: A Sourcebook
She has also set up some nice stuff on their website at UW:
http://depts.washington.edu/chinaciv/

So here's some of the textbooks I read (and still own) from my Asian History courses at college. All are worth reading over, but you'll also want teachers to help you, to talk with historians from China, and eventually just to go to China and see a lot of stuff for yourself.

The Cambridge Illustrated History of China, by Patricia Ebrey.

Chinese Civilization: A Sourcebook, edited by Patricia Ebrey.

Quotations from Mao Tse-Tung, written by the man himself.

Fiction:

Balzac and the Little Chinese Seamstress, by Dai Sijie.

The Outlaws of the Marsh, by Shi Nai'An and Sidney Shapiro.

The Three Body Problem, by Cixin Liu and Ken Liu.

These are a relatively good start to help you get a grounding in China's history. Everyone in this thread has also given some good suggestions. And visit /r/askhistorians; they'll have some better sources you can check out.

Perry Link, Richard P. Madsen, and Paul G. Pickowicz, eds., Popular China: Unofficial Culture in a
Globalizing Society (Rowman & Littlefield Publishers, 2002)

It may be a little outdated, but it gives a great look into modern Chinese cultural trends.

Chinese Civilization: A Sourcebook by Patricia Ebrey has great primary sources if you want to learn about Chinese culture that way, and it stretches all the way back to ancient times.

Yakuza: Japan's Criminal Underworld by David Kaplan and Alex Dubro is a great book to read if you want to learn about the Yakuza and how they have effected Japanese political history.