RCIA 487 gives the introductory rubrics for the Mass of receiving someone into Full Communion. “If the rite … takes place on a solemnity or on a Sunday” the Mass of the day is celebrated. I had not realized that on a weekday, the Mass “For the Unity of Christians” is suggested.
RCIA 488 reiterates the Mass choice, for the purpose of selecting readings, when appropriate. Number 489 describes the homily “express(ing) gratitude to God for those being received.” The three sacraments should also be “allude(d) to,” namely the Baptism the person or persons have already received, Confirmation, and the First Eucharist of the candidates.