"Sometimes we try to follow a theme, but often its just choosing something we haven't sung in a while, or something moving and reverent for post Communion like Panis Angelicus or Ave Maria."
I think perhaps, based on your response, that I have perceived a real difference. In the Divine Liturgy or the old High Mass, the chanting would have had a purpose as an integral and important part of the sacrifice and thus the words of the chant (which is really everything that is heard in a Divine Liturgy and an old Hign Mass). Whether something was moving or reverent really wouldn't be the issue, though everything in a Liturgy should be moving and reverent.
"In the Divine Liturgy or the old High Mass, the chanting would have had a purpose as an integral and important part of the sacrifice and thus the words of the chant (which is really everything that is heard in a Divine Liturgy and an old Hign Mass)."
Right you are. The High Mass (Missa Cantata or sung Mass) had the Ordinary Chants for the people/choir(Kyrie, Gloria, Credo, Sanctus, Agnus Dei) sung, using one of several modes, at every Mass.
In addition to these, there were the Proper Chants (Introit, Graduale, Alleluia, Offertory, and Communion). These had their own melodies and varied from Sunday to Sunday and feast to feast.
All of these were integral to the Mass. The hodge-podge of banal songs we are burdened with in today's vernacular services are extraneous to the Mass itself. In almost all vernacular Masses these songs replace the prayers proper to the Mass itself for which vernacular "translations" exist.
These translations occassionally have some similarity in meaning to the Latin Propers from which they were "translated".