What is the logic behind Sephiroth's forms?
As you can remember (or according to this Wikia article), Sephiroth's goal is to become god-like being, gathering a lot of energy.

According to this article, actual name of Bizzaro Sephiroth is "Rebirth Sephiroth", and this is more like intermediate form in his transformation to something more powerful, than he was before. Initial stage of transformation can be seen, when Cloud's party visits Northern Crater for first time:

Safer Sephiroth is more like final form of his transformation (judging from this article, it is more correct to call it something like "Seraph Sephiroth"). It is unknown, if it is his desired form, but for sure it is closer to "god-like being", than Bizzaro Sephiroth, as it looks more like majestic angelic being.

As last resort in battle, Sephiroth tries to manipulate Cloud, and final, human form is embodiment of Sephiroth's impact on Cloud's mind, existing only in Cloud's head. And by defeating this image of Sephiroth, Cloud frees himself from this impact.