This list has been filled with wonderful discussion of the Propers of the Mass, so I thought you might be interested in how we use them in our little parish in Alabama. Here is the program for 23rd Sunday in Ordinary Time.
The Introit is printed on the cover with a translation. Now, it's not quite right to do an Introit and a Processional, of course, so we sing the Introit after the bells are rung 5 mins before Mass. There is a brief silence and then the Procession begins. This is for obvious reasons that people are very attached to the idea of a Processional hymn. So perhaps it can be said that we treat the Introit as a "suitable song."
Our alterntive is not to do it at all, and that makes no sense. Also, people really adore hearing the Introit. So this is an accomodation we make for existing realities.
We don't usually list the composers, simply because doing so introduces a nonliturgical focus on personality. (Another judgement call.) But in this program, the Gloria Patri for the Introit is from Thomas Tallis. The Ego Sum is G. Palestrina. The Anima Mea is a wonderful piece by Martin De Rivaflecha. The Communion verses are printed in English but sung in Latin.
The Psalm is straight from the Missallete in the pews. We sing with no instruments, a single voice on the verses. The hymns are a cappella as well.
So long as we are making progress...