Currently if one searches for Chinese history on project Gutenburg, one gets the following results:
A history of China., [3d ed. rev. and enl.] by Wolfram Eberhard
China Revolutionized by John Stuart Thomson
Lion and Dragon in Northern China by Sir Reginald Fleming Johnston
The Civilization of China by Herbert Allen Giles
Ti-Ping Tien-Kwoh: The History of the Ti-Ping Revolution (Volume I) by Lindley
The Awakening of China by W. A. P. Martin
Historic China, and Other Sketches by Herbert Allen Giles
The Fight for the Republic in China by B. L. Putnam Weale
Ancient China Simplified by Edward Harper Parker
China and the Manchus by Herbert Allen Giles
Which, if any of these, are worth reading today for the interested layperson? Which ones should get priority? Which ones are considered bad history by modern standards?
To put some dates on those books,
Broadly speaking, and by that I mean entirely speaking, I would not trust any of these as a secondary source. If you look at Weale's introduction, for example, he's trying to use recent history to demonstrate the innate intellectual superiority of the Japanese. While Eberhard's is the most recent of all of them, anything written before 1980 on Chinese history – with few exceptions – is so archaic as to be of very little reliability.
However, one reservation regards three of these: Lindley (1866), Giles (1875) and Johnston (1910), as these are all primary sources. Lindley's narrative alternates between discussion of the Taiping's wider context and his own experiences with them, Giles' 1875 work is based on his own travels, and Johnston was an administrator in Weihaiwei, the subject of his writings. Obviously, all three have strong agendas, but give us a personal perspective on the events and times in question. The others appear to largely be writing from a distance, even those post-1911 works describing the Republican revolution. That doesn't mean you can't use them as sources in themselves, but largely for understanding attitudes towards China in the Anglosphere, not for understanding China in this period.