The most beloved of people to the Prophet (peace and blessings be upon him) was Abu Bakr, then Umar, then Abu Ubaydah (may Allah be pleased with them)

It is narrated from Yahya bin Abd al-Rahman bin Hatib that Sayyidah Aishah (may Allah be pleased with her) said: When Sayyidah Khadijah (may Allah be pleased with her) passed away, Khawlah bint Hakim came to the Messenger of Allah (peace and blessings be upon him) and said: "Will you not marry?" He (peace and blessings be upon him) asked: "Whom?" She said: "If you wish, a virgin, and if you wish, a widow (or divorcee)." He (peace and blessings be upon him) asked: "Who is the virgin and who is the widow?" She said: "As for the virgin, she is the daughter of the person most beloved to you of Allah's creation, Aishah bint Abi Bakr; and the widow is Sawdah bint Zam'ah."
This hadith is sahih (authentic) on the condition of Imam Muslim, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Abdullah bin Shaqiq; he said: I asked Sayyidah Aishah (may Allah be pleased with her): "Which of the people was most beloved to the Messenger of Allah (peace and blessings be upon him)?" She said: "Abu Bakr, then Umar, then Abu Ubaydah bin al-Jarrah (may Allah be pleased with them)."
This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it.

It is narrated from Abu Arwa al-Dawsi (may Allah be pleased with him); he said: I was sitting with the Prophet (peace and blessings be upon him) when Sayyiduna Abu Bakr and Umar (may Allah be pleased with them both) appeared. Then the Messenger of Allah (peace and blessings be upon him) said: "All praise is for Allah, who has supported me through these two."
This hadith is sahih (authentic) in its chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Hudhayfah bin al-Yaman (may Allah be pleased with him) that he said: I heard the Messenger of Allah (peace and blessings be upon him) saying: "I had resolved to send men to the various regions to teach people the Sunnahs and the obligatory duties, just as Isa ibn Maryam (peace be upon him) sent the disciples." It was said to him (peace and blessings be upon him): "Why do you not send Abu Bakr and Umar (may Allah be pleased with them both)?" He (peace and blessings be upon him) said: "I cannot do without the two of them. In the religion, these two are (to me) just like the hearing and the sight."
Hafs bin Umar al-Adani is alone in narrating this hadith from Mis'ar.

It is narrated from Sayyiduna Abu Bakr (may Allah be pleased with him) that when this verse was revealed to the Prophet (peace and blessings be upon him): "Indeed, those who lower their voices in the presence of the Messenger of Allah, they are the ones whose hearts Allah has tested for piety" [Surah al-Hujurat: 3], Sayyiduna Abu Bakr (may Allah be pleased with him) said: I made it binding upon myself that I would speak to the Messenger of Allah (peace and blessings be upon him) only the way one speaks a secret (in a very low voice).
This hadith is sahih (authentic) in its chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.