The Sunnah is to wash the private part before starting ghusl, as is indicated by the report narrated by al-Bukhaari (276) and Muslim (317) from Ibn ‘Abbaas (may Allaah be pleased with him) who said: Maymoonah said: I brought the Messenger of Allaah (peace and blessings of Allaah be upon him) water to do ghusl and screened him with a cloth. He poured water over his hands and washed them, then he poured water over his left hand with his right and washed his private part, then he struck his left hand on the floor and wiped it. Then he washed it and rinsed his mouth and nose, and washed his face and forearms, then he poured water over his head and all over his body, then he moved aside and washed his feet.
If someone touches his private part after that or washes it again, then to be on the safe side, he should do wudoo’ after he finishes ghusl, because the majority of scholars are of the view that touching the private part invalidates wudoo’. This has been discussed in the answer to question no. 82759.
And Allaah knows best.