Hello AskHistorians!
I've been reading Lewis' The early Chinese Empires: Qin and Han and it is a terrific read! I found it to be deeply informative and easily readable (and affordable too!).
If I can make one criticism is that it doesn't go in too much in depth with the structural organisation of the Qin-era army or other warring states forces. Lewis mentions about the implementation of Legalism and the subsequent conscription of the entire population to feed the Qin king's ruthless ambitions.
But that did not tell me of the more specific bits of the Qin army. How did the peasants get mobilized? How did they get trained? How long wes their mandatory service? How were they put into units? How did they get promoted? Was this truly an "imperial" army? And much much more.
I found The First Emperor: China's Terracotta Army to be more informative than The Early Chinese Empires, since the latter is more of a generic overview while the first goes into the details.
I don't have the book on hand but I can give you the gist of what it says.
Basically the peasants were grouped into households of tens, or rather tens of households. I can't remember which at the moment. At the age of 17-19 they would be conscripted into the army for three years of service. Ranks were awarded based on how many heads a soldier could collect. Again, I don't have the book with me, but I remember it was something like 3 heads for a first promotion, 10 heads for the next, and something like 50 for the third. The book also said that men would often willingly enlist in the army since soldiering became the only way to rise in Qin society.
Formations aren't talked about much because there aren't any surviving texts about them. Everything we know we base off of the Terracotta Army's arrangement and structure.
Although I don't trust the findings on army formation due to the lack of forthcoming information, it's very clear from how the Terracotta Warriors that the Qin did have formations, with ranks of dagger-axes, swordsmen, bowmen, and chariots.
For further reading:
The First Emperor: China's Terracotta Warriors
edited by Jane Portal
https://www.goodreads.com/book/show/1506650.The_First_Emperor?ac=1
The Terracotta Army and the Birth of a Nation
by John Man
https://www.goodreads.com/book/show/2233771.The_Terracotta_Army?ac=1
Records of the Grand Historian: Qin Dynasty
by Sima Qian, Burton Watson (translator)
https://www.goodreads.com/book/show/9032.Records_of_the_Grand_Historian?ac=1