It was narrated that 'Aishah (may Allah be pleased with her) mentioned:
"The Messenger of Allah (ﷺ) used to like to start with the right whenever he could, when purifying himself and when putting on shoes or combing his hair." (One of the narrators) Shu'bah said: Then I heard Al-Ash'ath in Wasit, saying that he liked to start with the right, and he preferred that in all his affaris. Then I heard him in Al-Kufah saying that he liked to start with the right whenever he could."
Arabic/English book reference: Vol. 1, Book 1, Hadith 112