For pre-20th century China, probably the best set of intros to get for a balance between comprehensiveness and conciseness, and with a good balance of political and social history as well, is Harvard's History of Imperial China series, which consists of six books, divided as follows:

• Qin and Han
• 'Northern and Southern Dynasties' (Three Kingdoms to Sui)
• Tang
• Song (plus Liao, Jin, and Tangut Western Xia)
• Yuan and Ming
• Qing

Each of them does a mix of chronological political history and thematic coverage. They're all around 15 years old so I suspect that particularly the earlier volumes may be a little out of date, but the Qing volume at least, which covers my speciality, is still largely up to date as the field isn't quite undergoing quite the same levels of paradigm shift that had been the case c. 2000.

Here are my tips for finding information on any subject not just the Far East:

1. Look up for JSTOR "X" such as JSTOR China bibliography, JSTOR Japan foreign relations with China or JSTOR Ming commerce as three examples relevant to your question.
2. Go to Wikipedia and scroll all the way down, the articles have pretty good bibliographies.
3. Footnote mine any books you have, they'll have bibliographies in the back too.
4. Go to your local library and bookstores. I find better books in used bookstores from experience.

The Far East isn't an area I research a lot about but here are some books I've read about Japan & China:

- Cambridge Illustrated History of China(Other Cambridge histories are good too, I use them a lot and both China & Japan have them.)

- A History of Modern Japan: Revised Edition(Probably pretty outdated but I found it fine as an overview of all the major events)

- The Battle for China: Essays on the Military History of the Sino-Japanese War of 1937-1945

- The Making of Modern Japan