I am not at all familiar with psalters and psalms
Now you're obligated to a lesson of Catholic liturgy
Better brace yourself!
You see, during a mass, there is a segment where psalm is read, if no singers are present. If there are, it should be sung, and if there's a organist playing, it's on them.
This is how the psalter looks like:
The text of psalms is always the same, it's the 150 psalms from Bible, or sometimes also verses from other books. The melodies composed vary, this one is work of mr. Korejs, who is still active if I'm not mistaken, so he has the luxury of having an
internet database of his works.
From the database:
In the book, there are only the melodies, in the PDFs from his site it's harmonized as well. If I'm in rush, I use these, otherwise I try to harmonize myself or use psalter of my teacher, where he did harmonized it himself, just with chord marks, but it's enough. Psalms are pretty good place for improvisation, too, one of our organists makes the melodies up as he goes
There are more segments of the mass where the sung texts are always the same, but with different melodies and compositions from different people. In our country we have four such legends, Olejník, Bříza, Eben and Pololáník, I use the Bříza's compositions when I play during the mass. If my name could be someday next to theirs, ohoho, what a legacy! My compositions would be played for years to come.
As you've written about the way you start off from melody or chords, yeah, I have similar ways, no set preference. I think I've written about it in my first post...
Also been improvising in middle of songs using their chords, getting pretty good at it, and I see my own style shaping there. I turned Rick's Astley's Never Gonna to some medieval folk song, it's pretty hillarious.