The Order of Christian Funerals provides some background on Funeral Mass Readings:
In every celebration for the dead, the Church attaches great importance to the reading of the word of God. The readings proclaim to the assembly the Paschal Mystery, teach remembrance of the dead, convey the hope of being gathered together again in God’s kingdom, and encourage the witness of Christian life. Above all, the readings tell of God’s designs for a world in which suffering and death will relinquish their hold on all whom God has called his own. A careful selection and use of readings from Scripture for the funeral rites will provide the family with an opportunity to hear God speak to them in their needs, sorrows, fears, and hopes.
In the celebration of the Liturgy of the Word at the funeral liturgy, the Biblical readings may not be replaced by nonbiblical readings. But during prayer services with the family nonbiblical readings may be used in addition to readings from Scripture.
– Order of Christian Funerals, General Introduction, nos. 22-23
With that in mind, attached are copies of approved readings during the Funeral Mass. These can be used by the family to help them select which readings they would like to use. The first reading will be one selected from the Old Testament, the second reading is taken from the New Testament, and finally there is a Gospel reading to be selected (for Funeral Masses held during the Lenten season, both the first and second readings are selected from the New Testament). Once selected, if a family member will be saying either the first or second reading, a copy can be printed off to practice with. The family will share their selections during the funeral planning meeting.
The family is also encouraged to select the Psalm to be used during the Funeral Mass. Depending on the selection, this may be either read or sung by the choir. You will find a link for the various psalm options below. The family will share their selection during the funeral planning meeting.