Alma 34:27 - How does God expect us to pray?

I have noticed a pattern of prayer in the scriptures. In Alma 34:27, God tells us to pray for our own welfare, and then to pray for the welfare of those around us. This pattern also appears in Enos 1:4-9, where Enos cries unto the Lord "in mighty prayer and supplication for mine own soul . . . all the day long" and then, once his sins have been forgiven, he pours out his "whole soul unto God" for the welfare of his brethren. It appears that God wants us to take care of ourselves first so that we can better serve those around us.