What are the origins of the Our Lady of Grace statues?
Our Lady of Cambray (Statue) also known as Our Lady of Grace is commemorated on July 5. This is the origin of the style of statue the question is asking for:
In the year 1472, the statue in the shrine of Our Lady of Cambrai was dedicated by Peter de Ranchicourt, the Bishop of Arras. The statue at the shrine is known as Notre Dame de Grace et Cambrai, or Our Lady of Grace at Cambray, and is a famous and popular image of the Blessed Virgin. It depicts Mary standing atop a globe, with her hands down at her sides so that grace can fall from her fingertips upon her children.
There is also a miraculous icon of the Blessed Virgin holding her Divine Infant in a tender embrace. The image is said to have come to Cambray from Rome in about 1440, and it is ascribed to Saint Luke the Apostle. This icon is also known as Our Lady of Grace, and is considered the patroness of Cambray. The icon was crowned in the year 1894, and is proudly taken through the streets of Cambray in procession on the eve of the Assumption each year. - Our Lady of Cambray
This predates the Miraculous Medal by 4 centuries!
Our Lady of Grace is commemorated on February 7.
Among the many miraculous images of the Mother of God through which she deigns to grant her favors, there is one in the monastery church of the Carmelites in Vienna, entitled the Mother of Grace, or Our Lady of Grace, also known also as Our Lady of the Bowed Head. - Our Lady of Grace
In general, the expression Our Lady of Grace is of medieval origin, especially well known in France, connected frequently with the Marian sanctuary of Cambrai, France. However, the roots of this title are much older. They are of biblical origin where Mary is called kecharitomene: the fully-graced one, the all-graced one (Lk 1:28).
Our Lady of Ipswich (also known as Our Lady of Grace) was a popular English Marian shrine before the English Reformation. Only the shrine at Walsingham attracted more visitors.
There was a time when England was known as 'Our Lady's Dowry'. Anglo-Saxon England sheltered many shrines to the Virgin Mary: shrines were dedicated to her at Glastonbury in 540, Evesham in 702, Tewkesbury in 715, Canterbury in 866, Willesden in 939, Abingdon before 955, Ely in 1020, Coventry in 1043, York in 1050, and Walsingham in 1061. By the High Middle Ages there were sixteen shrines to Mary in Suffolk alone.
About half of the medieval churches in Suffolk were dedicated to St Mary under a particular title or devotion. Churches not dedicated to Mary, would have contained a Marian shrine, generally at the east end of the south aisle. Some shrines became so popular that they were translated to buildings of their own. This may be how the shrine of Our Lady of Grace came to be. During the High Middle Ages, the shrine of Our Lady of Grace was second only to that of Our Lady of Walsingham. - Our Lady of Ipswich
As for Our Lady, Mediatrix of all Graces this statue may be the oldest on record that still exists (12th century):
Our Lady, Mediatrix of All Graces, now known under the double title of Our Lady, Mediatrix of All Graces and Our lady of a Good Death at Fontgombault Abbey. In Mary's hand we can notice the fruit of her graces she is offering to her spiritual children within the mystical body of Christ.
Further reading can be done with the following articles:
Our Lady of Grace
Shrine of Our Lady of Grace, Protectress of Marriages and Families