I have scoured the internet and about every historically accurate website out there on Condottieri, better known as the hired armies of Northern Italy from the middle ages to renaissance. I have figured out a good number of the main Condottiero and historical references to their role in shaping the Italian City States and the Papacy. What I am lacking is any references to their military structure, their condotta (or contract), how much power they are allowed to enact representing a city-state, what weapons they used, what armor they wore, what they did outside waging battles, did they have a coat of arms, military tactics (got some comments from Machievelli but nothing specific), or basically anything that would give a deeper understanding to who these people were?
I find it strange they played such an important part in one of the most important places of the renaissance but they are grossly overshadowed by the Templars, French, Germans, and Spanish countries.
There is some good background information in William Caferro, John Hawkwood: An English Mercenary in Fourteenth-Century Italy, (JHU Press, 2006) particularly chapter 3, "Italy and the Profession of Arms." Caferro notes in the introduction that Hawkwood was known in the 19th century as "the last of the foreign condottieri or the first of the Italian ones," so though the time frame might be a bit early, the scope of the background information has the later cases in mind as well. It talks about the organization and hiring of companies, the scope of contracts, rules of plunder, relationship between soldiers and employers, and so forth.