Asked a few days ago if it was alright to ask after good books on a particular topic, so here goes: I'm interested in the Qing dynasty, as it coincides with the period in US/European/world history I'm most interested in (I've got this strange infatuation with Queen Anne's War). Plus, we don't seem to get any education in the US on Chinese history, which seems silly to me since they're such a large nation and have been writing things down for years.
There's a book in the sidebar list on the Boxer Rebellion,and I'm currently reading a pretty interesting book on the Taiping Rebellion. I'm more interested in events before this however, maybe pre-1850? Or just a general period/dynasty book. After I feel like I've exhausted the Qing period, I hope to move into Sun Yat-sen and Chiang and Mao and the 1911-1950 period, but it seems like there's a lot of literature on that time which is a lot easier to find.
For a general overview of modern Chinese history I personally liked The search for modern China by Spence, it covers Chinese history in a fairly well from 1800-1990.
I would echo DeSoulis' sentiments of Spence's lengthy but fascinating 'The Search for Modern China'. He is thorough and certainly covers all the periods mentioned in your post - the one drawback I find is that he is a little (a very little) focused on role of the international involvement in perpetuating change in China. Though international involvement is important I personally err on Fenby's shade of grey which focuses a little more on the internal schisms and contradictions within China.
John Fairbanks' 'The Great Chinese Revolution 1800-1985' is another readable introduction. While lacking and sometimes showing its age in places it really hits on interesting informative niches for pages at a time - which is lovely to summon a broader picture of the Qing state. It is much better pre-1945 than post 1945 where, again, its age shows slightly.
For post 1880ish Johnathan Fenby's 'The History of Modern China: The fall and rise of a great power' is very good at the internal political forces shaping China - and goes beyond simply leaving Sun Yatsen as an icon of democracy and rather looks more into the fractious nature of Chinese nationalist democracy (with an eye to explaining Chiang Kai Shek's rise)
I find anything by Rana Mitter is good for post 1920ish even if he does oversimplify certain parts.
May I also be so bold to recommend some alternative mediums? On EdX there is a great 9 part lecture series on The History of China for over 1000 years. It's by Harvard and really good for a broad overview with useful discussion rooms to reflect finer points. Its section about the Qing dynasty is particularly excellent.
I would also suggest BBC4's wonderful 'In Our Time' which has a number of great programmes with 3 leaders in the field discussing specific areas of Chinese History, they have great episodes on the Opium Wars, Boxer Rebellion and Sino-Japanese War.
There are lots more specific works but it seems (correct me if I am wrong) you want to get a broad sense of the dynasty and period rather than a particular interest on, say, rural village life in Wuhan province.
EDIT: Grammar
A couple selections from my Ph.D. comprehensive examinations:
Peter Perdue, China Marches West: The Qing Conquest of Central Eurasia
Lynn A. Struve, ed., The Qing Formation in World-Historical Time
The first is, as the title suggests, an account of Qing imperial expansion into Central Asia. The second is more of a re-conceptualization of how the Qing Dynasty fits into the "early modern" world.