The Lenten tracts.

I second the Offertory verses. The Offertories are usually the most difficult part of the propers anyway. The verses are often more so.

I second the offertories - and some of the Alleluya verses. There is, of course, that famous tour de force, the offertory, Jubilate Deo, for Epiphany II and Easter IV (old kalendar) - see LU p. 486, or Easter V (new kalendar) in GTriplex - see p.227. The most elaborate (and haunting) chants, typically, are the graduals and tracts. The tracts are amongst the most ancient of the chant repertory, and are said to exhibit Byzantine and other Eastern borrowings and influences.

In your situation I would make it a point to choose elaborate chants from the joyful seasons' repertory - so as specifically to avoid transmiting the chant=penitential syndrome to a chant neophyte.

Hmmm... I would posit that neums are not what make a chant piece challenging, and unless you are tying the notation back to Laon / Gallican scripts, I'm not sure of the purpose of choosing something that is nothing more than a big melisma.

Vocally challenging? Ad Libitum Gloria I. Wide range, lots of potential challenges with intervals. Some of the Sequences are challenging initially - including Sequences no longer in use (Ave Virgo Serena, for example). In addition to whatever vocal challenge there is, these examples demonstrate that not all chant is melismatic - and it might be useful toward a discussion of the importance of text and the difference interpretatively between melismatic and syllabic driven phrases... because even in Graduals and similar chants, there is often a mixture where the author may be making a statement by using syllabic phrasing in places.

I would include the Gradual / Alleluia from Advent I. The Gradual is a perfect illustration of the importance of the custos - and is the only example I'm aware of where there is a transition mid piece from FA clef to DO clef (in a Mode II, no less!). Doing a Gradual / Alleluia allows you to discuss the value of choosing a starting pitch that allows a seamless transition - will you transpose the scale? If you don't, what does that mean in terms of the range of either the Gradual or the Alleluia?

It would be helpful to include a Marian anthem (there are other examples, but most prevalent and easiest to find in the Marian anthems) that has a TE Key Signature. That can provide a discussion of why TE, the nature of key signature in chant notation, the rules that govern accidentals. I would probably follow that with a piece (Introit of Holy Cross / Holy Thursday is a good example) where every TI is flatted but not by a key signature, and then by a piece where there are both TI and TE (maybe the Offertory from Pentecost XXIII? Perhaps the Obtulerunt responsory or the Introit - both of Candlemas?).

It might be useful to demonstrate melodic elements that are found over and over - and to illustrate MJO's point, found in both chants from moments of pain as well as joy... Perfect example might be the Gradual / Tract of the Requiem - found in the Canticles of Holy Saturday; chants of Easter Sunday, of the Nuptial Mass, etc..

Good luck with your student!

Some of the mode IV Holy Week responsories. Well beyond, for the most part, what one encounters in the Mass propers.

The Communion from last Sunday, Passer Invenit. That thing is a beast (no pun intended).

Passer invenit always reminds me of a turtle dove, cooing.

...always reminds me...

And it was most likely intended to. This is not the only example of 'word painting' in chant - and it should gainsay all those who insist that there isn't any.

Not only challenging, but there is hardly another chant that is as heart-rending as Pascha nostrum - the alleluia verse for Easter Day. I'm never quite sure whether it is an ecstatic cry of joy over our Christ's triumph, or a cry of profound grief in response his ordeal. Perhaps it is both.