Interested about finding out more about the history of the Papal States and Popes.
Was it the Pope or the Holy Roman Emperor in fact the head of the Papal State? Did the Papal state ever maintain a regular army? Were the Swiss the primary(or only) mercenaries within the Papal State's army?
Which Pope(s) were the "Holiest of Fathers" and which should(if any) be considered the least holy of them all?
You need to be more specific since the Papal States lasted over 1,000 years it obviously had different governmental and military structures. The earliest "Papal States" were ruled by essentially the Roman aristocracy, most notably in the awesomely named period "pornocracy."
In 962 when Otto I conquered the Kingdom of Italy, the HRE obviously became interested in the Papal States. The Otto-Papal treaty, Privilegium Ottonianum made things dodgy, the Papal States were made kind of like an independent client state. The actual influence varied with the Emperor's power projection. In nomine Domini in 1059 began the process of breaking Imperial authority which "ended" with the Concordat of Worms in 1122.
Warfare again changes through the ages. Pope John X is the first known pope to personally command and fight in a war though others (Leo IV comes to mind) were present during wars as a kind of morale support/figurehead. Generally the rule of thumb was that Cardinals would lead the papal armies. Especially early on the Roman militias provided the core supplemented by various allies. John X's campaign, for example had the allied army consisting of Lombards, Byzantines, and various independent Italians.
Even in their heyday the Swiss were never the only mercenaries. The Corsican Guard is one of the more (in)famous of these. Italians were always a significant presence among the mercenaries.
The relative "holiness" or lack thereof of individual popes is dependent upon who is making the judgment. The Catholic Church thinks 81 of the 265 popes were sufficiently holy to be named saints. On the opposite side, I know Pope Liberius and Pope Honorius were declared heretics. Several popes were involved in various sexual exploits and power politics which depending on your moral code might not seem that bad.