I don't like the origin stories where humans end up being responsible. We already have a galaxy with the conceit that all important events of the last few centuries are pioneered by humans, we don't need the Borg to have been the fault of humans too. Let something important in the galaxy not revolve around us.
The motives of the Borg are made pretty clear in the series. The goal is to attain perfection by adding the particular characteristics of every race to their own. This is a little different from the Nazis because the Nazis believed their culture was inherently perfect and everything else needed to be destroyed. The Borg believe they are not perfect yet but can attain perfection by absorbing others.
As for the origin story. I tend to think they started when a biological species gave themselves technical augmentation to improve themselves, and then wanted to spread the gospel of perfection to the rest of the galaxy. Though the 'center of the universe' explanation is an interesting proposal.