How does one reorganize one's entire Aperture library from scratch?
By default, there is not any magic when importing photos to aperture.

Probably at that point, what it might be confusing is that Aperture has transformed your iPhoto albums to folders/projects, which are not what you exactly want.

My advise would be to create one project, move all your images there, delete all other projects/folders, and then create new projects as desired.

Furthermore, you can find a lot of articles of how you may use projects/folders to organize your photographs, like this one.