The Prophet (may Allah's peace and blessings be upon him) preferred beginning with the right side when wearing his sandals, combing his hair, purifying himself, and in all of his affairs

An-Nawawi said: This is a constant rule in the Shariah: that in doing any activity worthy of honor, like wearing a garment, lower garment, and sandals, entering the mosque, using the Siwāk (tooth-stick), applying kohl, clipping the nails, trimming the mustache, combing the hair, plucking the armpit hair, shaving the head, making Taslīm in prayer, washing the parts to be washed in ablution, leaving the lavatory, eating and drinking, shaking hands, touching the Black Stone, etc., it is recommended to start with the right side. As for the opposite activities, like entering the lavatory, leaving the mosque, blowing the nose, Istinjā’ (cleaning oneself after urinating or defecating), putting off garment, pants, and sandals, and the like, it is recommended to begin with the left side. This is all due to the high status and honor of the right side.
"The Prophet (may Allah's peace and blessings be upon him) preferred beginning with the right side" includes beginning activities with the right hand, the right leg, and the right side, and receiving anything from the right side.
An-Nawawi said: Know that it is not recommended to begin with the right side in washing some parts of ablution, namely the ears, the hands, and the cheeks. Each pair of them should be purified at once. If this is not possible, like in the case of a one-armed person, he should begin with the right side.