Is it better to complete the marriage with a girl who had transgressions in the past but has repented, taking into consideration the initial rejection of her by the family, and the suitor's feeling of distress, jealousy, and inability to forget her past, or is separation better to avoid wronging her in the future?

A correct repentance erases what came before it. A repentant person is not punished for their sin. It is not permissible to shame a girl for her past after her repentance; rather, her current state should be considered. A feeling of apprehension after performing Istikhara (prayer for guidance) does not prevent marriage, as the preponderant opinion is that one should proceed with the matter after Istikhara unless Allah diverts them from it, and a feeling of contentment is not a prerequisite. It must be noted that a suitor is a stranger to his fiancée until the marriage contract is concluded. If the whispers and fears dissipate, then praise Allah and proceed with the marriage. If they persist, there is no sin in breaking off the engagement.