In John's Gospel Martha is shown as an ideal believer with the most developed faith of the entire gospel when she declares: "Yes Lord, I believe that you are the Messiah, the Son of God, the one coming into the world” (11:27). Patristic writings, interpreting this statement, understand Martha as "a second Peter," that is, a foundation of faith (5th C writer Pseudo-Eustathius' Homily on John 12: 12, 141-145). In the Coptic text of the 2nd Century Epistula Apostolorum, Martha is sent as first apostle of the resurrection.
In a late second or early third century homily on the Song of Songs, Hippolytus describes Martha and Mary of Bethany as "apostles to the apostles" since they are witnesses to the resurrection (25,6).
In a 2009 book, Martha from the Margins: The Authority of Martha in Christian Tradition by Allie M. Ernst, this tradition from Hippolytus (and the patristic interpretations of the first paragraph above) are explored. In Hippolytus Martha is named first. In Hippolytus' commentary, the Easter narrative is told from the point of view of the women whose voice is heard by way of the Song of Songs.
The book is a version of the author's 2007 Queensland PhD thesis. A review of this book that came out in March 2001 by Joseph Oryshak of York University is here. He concludes:
Ernst’s methodology, which featured a dynamic reading of church orders and a balanced weighing of literary/historical texts with other types of sources (iconography, liturgical works, and hymnody), allow her to present a more expansive perspective of Martha within early Christianity. Hopefully, this approach will be used by others in the future. In Martha from the Margins, Allie M. Ernst succeeds in rescuing Martha from obscurity and in highlighting the prominent role she held in various early Christian circles.
Unfortunately the book is prohibitively expensive and will be accessible to most people only through libraries or online summaries. But it is essential to consult this new material. Books on women in the NT might (wrongly) name Martha "neither apostle or disciple" (see also this link to The Catholicism Answer Book of 2007 where Mary and Martha are described as loyal followers but not chosen as apostles--the text of Hippolytus's Commentary on the Song of Songs above presents a different interpretation of their roles) or omit all references to Martha and Mary for various reasons (although titles suggest they cover all gospel women) or consult only canonical materials.