I know, there are plenty of threads on this topic in the general discussion as to which of the playable clans people like using in the single player campaign. This one is specifically for the historians.
I stand by my belief that one cannot fully appreciate Shogun 2 unless they know some Japanese history. The reason is the Sengoku Jidai is just wealthy in terms of colorful characters, whether it's Takeda Shingen who overthrew his own father, Uesugi Kenshin who became the lord of his own lord, or Oda Nobunaga who seemingly assassinated everyone who looked at him funny.
So this certainly isn't an easy choice but my personal favorite might be the Amako clan. The reason for this is their especially psychotic family politics. First off, for a time they were the dominant power of the Chugoku region (aka Western Honshu), and much of their military history was a back and forth against the Ouchi clan and their vassals, the Mori. Nonetheless, factions appeared within the clan and in 1554, Amako Haruhisa ordered the execution of his uncle, Kunihisa, several other family members, and a number of prominent generals. This was done ostensibly for Haruhisa to consolidate his hold within the clan and in hindsight, the intra-family purge seemed counterproductive, just as the Otate no Ran for the Uesugi, although the extent to which is contributed to their eventual fall is surely a matter of interpretation.
But fall they did to the Mori, and here entered the other interesting character of the Amako clan, their retainer Yamanaka Shikanosuke. He vowed to restore their clan to their former power, found Amako Katsuhisa (who fled the purge to become a monk), and with the support of Oda Nobunaga recaptured part of their territory. However, when the Mori counterattacked, Katsuhisa committed seppukku and Shikanosuke was captured and executed.