What are some good Morning Prayers?

The answer to your question about morning prayers is that, after the morning offering, it is good to say the following prayer to the Holy Trinity - the prayer given at Fatima.

"Most Holy Trinity, Father, Son, and Holy Ghost, I adore thee profoundly, and I offer You the most precious Body, Blood, Soul and Divinity of Jesus Christ, present in all the tabernacles of the earth, in reparation for the outrages, sacrileges, and indifference with which He Himself is offended.  And through the infinite merits of His Most Sacred Heart and of the immaculate heart of Mary, I beg of You the conversion of poor sinners."

Sub Tuum Praesidium

We fly to thy patronage, O holy Mother of God! despise not our petitions in our necessities, but deliver us from all dangers, O ever glorious and blessed Virgin.

Dedication to the Blessed Virgin Mary

My Queen, my Mother.  I give myself entirely to thee; and to show my devotion to thee, I consecrate to thee this day my eyes, my ears, my mouth, my heart, my whole being, without reserve.  Wherefore, good Mother, as I am thine own, keep me, guard me, as thy property and possession.

Short Prayers to the Virgin

Sweet heart of Mary, be my salvation. My Mother, preserve me this day from mortal sin. Mother of love, of sorrow, and of mercy, pray for us. My mother, my trust. Mary, Virgin Mother of God, pray to Jesus for me. In thy conception, O Virgin Mary, thou wast immaculate, pray for us to the Father, whose Son Jesus Christ conceived of the Holy Ghost thou didst bring forth. To thee, O Virgin Mother, who wast never defiled with the slightest stain of original or actual sin, I commend and entrust the purity of my heart. O Mary, conceived without sin, pray for us who have recourse to thee.