1) When one removes his shoes, one should first remove the left one, as this is honor for the right side, that the shoe should stay on the right foot for longer. (Shulchan Aruch and Mishne Berura 2)
2) When a person washes himself, he should first wash the right side. If he washes and anoints his whole body, he should start with his head as it is considered like the king over all the limbs. (Mishne Berura ibid)