Simply throwing yourself at 'far east' history would, IMO, be enormously unhelpful if you want to gain anything other than a very basic and probably quite unhelpful baseline of understanding within any of the uncountably numerous fields of history which could be broadly tied to or encapsulated within the term 'far east'. You mention China and as someone who specialized in China during my time in school, I can say that it might also be unhelpful to even try to start perusing the history of even one specific period of Chinese history for a number of reasons. For starters, there are many periods of Chinese history which can quickly overwhelm an amateur, but also just jumping into say, late Ming dynasty social history, would leave you sorely wanting for historical context and connections to the themes of broader histories not just throughout China but also to contemporaneous world histories if you don't have a solid foundation to build upon.

It might be best to read broadly at first. I always recommend to prospective amateurs some form of primer on the Confucian canon not only because of the enormous influence of the Four Books and Five Classics on Chinese history, but also because the overwhelming majority of Westerners have... no meaningful exposure to the canon and the very basic tenets encapsulated within. Daniel Gardner has a neat, elementary, and concise introduction to the Four Books in his The Four Books: The Basic Teachings of the Later Confucian Tradition. He also has a work on the orthodox commentaries of the Song dynasty Neo-Confucian philosopher Zhu Xi if you're interested. Jonathan Spence's The Search for Modern China is probably one of the definitive primers for early modern-modern Chinese history and it has an accompanying documentary collection to go along which is filled with primary sources translated into English. There are also the Cambridge Histories which are great as well. The Cambridge histories are definitely more comprehensive than Spence's work and they also cover most of Chinese history whereas Spence starts with the late Ming, but both are still very excellent works. Lastly, Harvard also has its own six (?) volume set on Imperial Chinese history although I can't vouch for the work as I have never personally used it. From there, you have plenty of routes to take. As a history undergrad, I ended up going pretty deep down the rabbit hole of Ming history with all of my capstone work and thesis work done on the Ming dynasty's social and cultural history. There are a huge number of excellent works that cover many eras of Chinese history, ranging from very well-known topics like the Treasure Voyages of the Ming, to far more obscure readings, such as governmental organization in various polities during the Northern-Southern dynasty period, or the late Ming dynasty book economy and printing trade in southern China. The key to really tying it all together though is being able to tie loose ends together and synthesize your own understanding well beyond simply memorizing dates and reign eras. Tying whatever history you choose to learn to other parts of the global historical web and creating your own understanding of a topic is really where you want to aim to be.

As a final note, make sure you pick good sources. I usually invariably recommend sticking to only university presses and reputable journal articles/book reviews for your sources since there are a LOT of questionable pieces floating around in the popular history genre. Expensive, but academic. There are definitely ways to circumvent the cost such as browsing bookstores or catching sales though. Princeton University's press has some solid sales, for instance, and the one they had this year tacked on a hefty 75% off thousands of items in their catalog. I think I spent about 300 dollars in one go on books and Chinese textbooks.