As for drinking, the sunnah is to give precedence to the one on the right, as al-Muhallab stated above. The hadith to which he alluded will follow, Allah Most High willing, (1771).
1556 — “I was commanded to use the toothstick until I feared for my teeth.”
Al-Tabarani recorded it in al-Mu'jam al-Kabir (3/155/2), and al-Diya, on his authority, in al-Mukhtarah (61/249/1), through al-Husayn ibn Sa'd ibn Ali ibn al-Husayn ibn Waqid: “My grandfather, Ali ibn al-Husayn, told me; my father told me; Ata ibn al-Sa'ib informed us, from Sa'id ibn Jubayr, from Ibn Abbas, from the Prophet, peace and blessings be upon him, with this wording.”
I say: This is a weak chain of transmission. Its narrators are trustworthy apart from al-Husayn ibn Sa'd ibn Ali ... for I have found no biographical entry for him, although they mentioned him among those who narrated from his grandfather, Ali ibn al-Husayn. Ata ibn al-Sa'ib had become confused in his narrations. Al-Tabarani also recorded it through his route in al-Awsat, as cited in al-Majma' (2/98), where it was deemed defective solely on his account. However, the hadith has corroborating reports that raise it to the level of authenticity:
The first is from Sahl ibn Sa'd, with the wording: “Gabriel continued urging me to use the toothstick until I feared for my molars.” Al-Tabarani recorded it in al-Kabir, and its narrators have been declared reliable, though there is disagreement concerning some of them, as al-Haythami said. I then found it in al-Kabir (6018/1), through Ubayd ibn Waqid Abu Abbad al-Qaysi, who said: Abu Abd Allah al-Ghifari narrated to us: “I heard Sahl ibn Sa'd attribute to the Prophet, peace and blessings be upon him, the wording: ‘Gabriel commanded me to use the toothstick until I thought I would become toothless.’” Ubayd is weak. I did not find the wording cited by al-Haythami in Sahl’s entry in al-Kabir.
The second is from Aishah, attributed to the Prophet, peace and blessings be upon him, with the wording: “I persisted in using the toothstick until I feared it would render me toothless.”