Praise be to Allaah.
The first khaleefah who succeeded the Messenger of Allaah (peace and blessings of Allaah be upon him) was Abu Bakr al-Siddeeq (may Allaah be pleased with him), according to the consensus of the respected scholars, because of the consensus of the Sahaabah who all gave their bay’ah (allegiance) to him. This was after an initial dispute between the Muhaajireen and Ansaar, then the Ansaar were convinced and gave their bay’ah to Abu Bakr, and they did not differ amongst themselves, and they did not hesitate in making a choice between Abu Bakr and ‘Ali (may Allaah be pleased with them both). None of the Sahaabah asked to give bay’ah to ‘Ali after Abu Bakr and before ‘Umar (may Allaah be pleased with him), and no one asked to give bay’ah to ‘Ali after ‘Umar – may Allaah be pleased with them all. The fitnah and differences arose because of the murder of ‘Uthmaan (may Allaah be pleased with him). The Sahaabah (may Allaah be pleased with them) accepted for their worldly affairs the one whom the Messenger of Allaah had accepted for their religious affairs, the one who had acted as the deputy of the Messenger of Allaah (peace and blessings of Allaah be upon him) in leading the prayers [when he was unable to do so – i.e., Abu Bakr].
With regard to what happened at Ghadeer: Ghadeer is the name of a well in a place between Makkah and Madeenah which is called Khum. The hadeeth was narrated by Imaam Muslim in his Saheeh (no. 2408) from Zayd ibn Arqam, who said: “The Messenger of Allaah (peace and blessings of Allaah be upon him) stood up and addressed us one day at a well called Khum, between Makkah and Madeenah. He praised Allaah and exhorted and reminded us. Then he said: ‘I am leaving among you two important things: the first of which is the Book of Allaah’ – and he urged us to adhere to the Book of Allaah, then he said: ‘And the people of my household (ahl bayti). I remind you of Allaah with regard to the people of my household, I remind you of Allaah with regard to the people of my household, I remind you of Allaah with regard to the people of my household.’” Zayd said: his wives are among the people of his household, but the people of his household who are forbidden to receive sadaqah (charity) after his death are the family of ‘Ali, the family of ‘Aqeel, the family of Ja’far and the family of ‘Abbaas. All of these are forbidden to receive sadaqah.” [abbreviated version].
His advice concerning the people of his household has to do with honouring and respecting them, and not exposing them to abuse or annoyance. This does not mean that they are to be given preference over others who are known through the texts to be more virtuous than them, such as Abu Bakr, ‘Umar and ‘Uthmaan (may Allaah be pleased with them all).