I posted a while back about the opportunity I had to chant the introit "Requiem in aeternam" and the "In paradisum" at a funeral in my parish.  When I mentioned to my pastor how well I thought of this experience and my pleasant surprise that it's been going on for a while now during funerals at our parish, Father mentioned his impression so far: 

The more cantors we can train to sing the Requiem and the In Paradisum the better!  I try to sing out as best as I can from down below.  I have them both pretty much memorized now.  In the four or five months that we have been doing these chants for all funerals I have not had one complaint.  I know [our music director has] fielded one or two.  However, one thing I have noticed about the mourners as we do the Requiem is that it has a calming effect on them and sets a solemn and prayerful tone for the Mass.  Whether the family is upset and weeping or raucous and disrespectful, as the Requiem sounds as they enter the church it transforms them to where they need to be emotionally and mentally and spiritually... it really shows the genius of chant within the liturgy.

Now the USCCB has come out with an advisory document on sacred music, upon which I will go into detail later on, but there is one section mentioning music for funerals.  Most of the recommendations they make comes from the Order of Christian Funerals.  I do not know the authority of this book, I thought there was another book called the Rite of Christian Burial, but at any rate there is no mention of the chanted introit "Requiem in aeternam" being appropriate for the procession, nor of "In paradisum" being a good choice for the final procession.  I have no idea what the Order of Christian Funerals is based on, but apparently it is not on the Requiem Mass.

In looking into music recommended for Catholic funerals a little further, I found this article by Lucy E. Caroll on the Adoremus website: Music for Catholic Funerals -- or, But Uncle Horace Loved that Song!  It makes specific recommendations from the Adoremus hymnal, but included among them are the introit and in paradisum from the Requiem Mass. 

For the record, when my time comes I hope it is possible to have a requiem Mass for my funeral (with the propers chanted in Latin) with all the fixings, including the Dies Irae sequence, and one thing I agree with the USCCB on is that it would be great to provide the congregation with translations of the Latin so they can appreciate the beautiful prayers expressed therein. 

Interested in the Requiem Mass Latin text, English translations, and scores?  Find them here: Canticum Novum Deceased Office.