The Prophet ﷺ used to love starting with the right side whenever he could, when combing his hair and when performing ablution.
عن النبي ﷺ: أنه كان يعجبه التيمن ما استطاع، في ترجله ووضوئه.
Bukhari narrated it in the Book of Dress (5926), and Muslim in the Book of Purification (268:67), both through the route of Shubah, from Ashath bin Salim, from his father, from Masruq, from Ayesha, who related it.