My strong impression is that the Offertory chant seriously needs some love from the Ordinary Form community. Most musicians don't even know that it exists and instead treat the offertory as a time to sing their favorite number, whatever it happens to be (like the "special music" of a Baptist service). You can find the official offertory chant in the Roman Gradual (or Gregorian Missal). For example, this week, the offertory chant is Scapulis Obumbrabit. "The Lord will overshadow you with his pinions, and you will find refuge under his wings. His faithfulness will encompass you with a shield."
Here is an MP3
But, you say, it is too short to take up the entire time during this period of Mass. Well, we are exceedingly fortunate these days to have access to a glorious book that I don't think I've even mentioned on this blog. It is the 1934 Offertoriale that has complete and composed Psalm verses for the offertory chant. You can buy it here.
This way you are permitted to extend this chant with fully three verses, the last of which has an astonishing melisma at the end. What a wonderful idea for the first Sunday of Lent!