The word "suits" can be interpreted in many ways. I will answer in the manner that seems most interpretive of the characters' personalities in this novel.
Genji is a spoiled paramour whose romantic conquests are legendary. When this novel was written, over 1,000 years ago, women were relegated to the role of being subordinate to men. In fact, one of the words for "wife" in Japanese, kanai, translates to "of the interior." Japanese women, especially women of elite status, rarely left their homes. Even with this understanding, it is difficult to separate our modern sensibilities from our interpretation of this text. Therefore, I would have to say that my choice of the character who "suits" Genji best stems from a sense of hopeful equality for women during a time when this was virtually nonexistent.
I believe the character who "suits" Genji best is the Rokujo Lady because she is the only woman who exacts revenge on Genji. Despite Genji's charm and obvious physical appeal, he is quite a heartless philanderer. In his philandering wake he leaves countless women heartbroken and many children fatherless, so when a woman is able to exact revenge on his heartless ways, I am bound to believe she is the woman he deserves. The Rokujo Lady's powerful spirit leaves her body and kills two of Genji's other lovers. She feels little or no remorse for her actions, mirroring Genji's lack of remorse for the destruction he causes with his philandering. She is more concerned with her reputation than with any feeling of wrongdoing in the murders. This also mirrors Genji's egotistical actions throughout the novel.