I think part of the problem is that we don't have an aesthetic. The Orthodox do have one. They ask themselves (on some level) what does it mean to be a parish in the ________ Orthodox church. Text and musical selections are generated (or dictated) as a result.

I am not sure that many ask themselves the question: "What does it mean to be a Latin Rite Roman Catholic?" Part of it may be that the Roman Rite has adapted itself to a number of cultures which were not originally Latin or Roman. Part of it may be that the reaction to the Second Vatican Council was far more aggiornamento rather than ressourcement which cut off the church from its aesthetic roots (whatever the documents said).

It would be interesting to see the question asked consciously and how it is answered.

I am going to be the unpopular one who says this, but we could avoid the whole question altogether and just use the GR: the Church has already done all of that work for you.

When restricted to the 4-hymn model, I've found that trying to incorporate the proper of the Mass into the programming is not viable, as the "crowd favorites" that people will sing generally have nothing to do with any of the texts of the proper. Sometimes they do, but most of the time, they don't. My thought is this: if you're going to use the proper of the Mass as a resource, just sing the proper. So, when I'm programming using the 4-hymn model, I concentrate on simply choosing songs that the congregation knows and can sing. I do try to put an emphasis on Eucharistic hymns, though.

When choosing motets, I favor Eucharistic texts over all others, but often there are motets that incorporate the text of the proper, and unless I'm mistaken, the general direction is to use only the text from the proper.

The main thing for me is that the Church has already done all of this work for us, and we don't need to select extraneous pieces to perform, unless you're selecting motets, choir anthems, or organ pieces, and even then, they should be somewhat in line with the proper that they supplement. A good example is de Maleingreau's "Low Mass For Christmas Day," for organ solo. Each of the processionals are thematically based on the proper chant melody for the day, but of course stylistically and idiomatically arranged for the pipe organ. It is a sublime work, and very enjoyable to play as well.

EDIT: CHGiffen below said what I could not: the Mass is not a concert, so the programming guidelines that your professor gave you do not apply. My professor gave us very similar guidelines, but I was a clarinetist and took band and orchestral conducting.

Bravo!
Well said, Charles!

And a word or two further.
There are aspects of church music programs which could or should take into consideration things like a balance of period musics as concerns the choir's repertory. One should wish to have in one's choir's accomplishments a representative sampling of motets and anthems and chants from all centuries and periods, not in the least neglecting genuine 'modern' (as opposed to 'contemporary music') masters. Ideally, chant should be well represented, with the Gregorian propers, if possible, regularly fulfilling their role and function. <> For the congregation one should wish to give them, also, as much chant as they are capable of singing, in addition to ordinaries subjected to excruciating musical standards, and genuine hymnody. The instrument of choice should be the organ, perhaps supplemented with brass consorts or such on solemnities.

As for historically informed performance practice, while I admire and recommend it highly for recitals and spiritual concerts, it should play a small, if any, role in the choral music sung at the mass. One would never wish to perform anything in such manner that it would seem artistically distracting; or not contributing to the profound spirituality of the mass. As Charles said so well, the function of music at mass is to make of the mass itself that continuous song, of which HF Benedict speaks, a seamless garment of song from Trinitarian Invocation to Dismissal, which it always should be. The mass is not the time to exhibit one's musicological pedigree. At least not chorally. Playing organ literature as voluntaries is another matter.

In choosing music for a given mass, some care should be taken to the end that all of it seems somehow related, meaning that there should be a rough continuum of complementarity in the music of that mass. The styles and performances should not be so divergent that the mass seems to be 'a little bit of this and a little bit of that', without any unifying aesthesis. This is obviously a very subjective sort of recommendation, but it is well worth keeping in mind. Nor is it meant to suggest a monotonous succession without any highs and lows, climaxes, emotional and intellectual arses and theses; even some liturgical sturm und drang when appropriate.

I recently gave a recital of chant based organ music. We did the chant accompanying de Grigny's Ave maris stella with pronounced 17th century French accents, very slowly, semi-measured and with trills at the cadences. This was much appreciated at this sacred concert. It would have been totally, utterly, out of place at mass.

By all means, sing Palestrina, Mouton, Perotin, and Howells, Britten, and Messiaen. But don't do period performances of them at mass. Sing them with a nod to the most tasteful choral aesthetics of our time - and you'll find no better examples of such than English cathedral choirs (including Westminster Cathedral!).

End of word or two.

The OP is great. Some thoughts:

1) My mentor, Gerre Hancock, did not like mixing styles of CHORAL music within a Mass, and preferred that you matched organ music to the choral as well. This was an ECUSA context (St. Thomas Church, 5th Ave.), but I think it's still decent advice.
2) I don't mind mixing and matching, but it depends on the day and the rep. Obviously, if one is doing a polyphonic ordinary, you would want to choose ONE, not a few of them in one liturgy.
3) It's a bit of a pastiche to do some parts of the ordinary in Latin and others in English; we do that at Chrism Mass since there are some within the presbyterate who have yet to be converted... ;)
4) Keeping to one style can be expensive, staff-wise: you need a director/organist who knows the rep and can pull it off, then singers, then a decent organ, then... This is why I am a little more pragmatic with mix-and-match.

I must say that some of these comments have given me quite a bit to think about, thank you very much!