Sengoku Jidai has kind of a magical place in the pop culture awareness of many westerners, but if you sit down and ask ten people what it "was" you'll get fifty different answers somehow. To some people it was a mad dash for supreme authority in the nation. To others it was a break down in central authority, resulting in a group of people, no longer bound by threat of intervention, using the chaotic opportunity to settle old scores. Other people see it as essentially a somewhat ad hoc civil war with a particular goal in mind.
I suspect a monolithic answer like "because of X, the samurai decided to fight a civil war with each other to decide who would rule the nation" is grossly over simplifying, but the kinds of sources readily available to a layman don't give enough insight to really command a solid opinion.
When someone thinks of Sengoku Jidai what should they think of as the defining features of the era? Why was it so bloody? What kinds of goals could we expect to command the agenda of your average daimyo? Was the era marked by a group of people who wanted supreme authority, or was the chaos of the situation such that some warlords decided to exert supreme authority in order to bring said chaos to a close? And most important what made Sengoku Jidai, as an era, culturally, economically, and legally different from previous eras in Japanese history?
I disagree with the perceived need to make one narrative over a period of Japanese history that span a century and a half. None of the view points you mentioned above is wrong. They are just different angles to view different time periods and locations.
When someone thinks of Sengoku Jidai what should they think of as the defining features of the era?
Warfare.
Why was it so bloody?
Because there was no restriction on the victim, that armies became very large as lords mobilized more people in order to win.
What kinds of goals could we expect to command the agenda of your average daimyo?
Hold onto and expand political power.
Was the era marked by a group of people who wanted supreme authority, or was the chaos of the situation such that some warlords decided to exert supreme authority in order to bring said chaos to a close?
Open to interpretation and not mutually exclusive.
And most important what made Sengoku Jidai, as an era, culturally, economically, and legally different from previous eras in Japanese history?
No other time in Japanese history was there a period of a century and a half of chaos and civil war.