The Prophet (ﷺ) used to like to start from the right side on wearing shoes, combing his hair and cleaning or washing himself and on doing anything else.
Sahih al-Bukhari Book 4, Hadith 34
← Previous Hadith That the Prophet (ﷺ) at the time of washing his deceased daughter had said to them, "Start from the right side beginning with those parts which are washed in ablution."

Sahih al-Bukhari Book 4, Hadith 33 Next Hadith → saw Allah's Messenger (ﷺ) when the `Asr prayer was due and the people searched for water to perform ablution but they could not find it. Later on (a pot full of) water for ablution was brought to Allah's Apostle . He put his hand in that pot and ordered the people to perform ablution from it. I saw the water springing out from underneath his fingers till all of them performed the ablution (it was one of the miracles of the Prophet).

Sahih al-Bukhari Book 4, Hadith 35