I have kind of a lot of questions here, but hopefully it makes sense what I'm getting at. What is the nature of the Psalter as a whole in terms of how it was meant to be used? I've always assumed that part of their function is teaching, but it's not as if there is a purpose statement attached to them. Are the Psalms meant to be didactic? Or are they simply a collection of Israel's "greatest hits" so-to-speak? Does it vary from Psalm to Psalm?
See this overview from jewishencyclopedia.com. The overview breaks out the Psalms into classes:
A more detailed analysis could probably add more classifications such as historical, epic, etc.
Psalms, like Proverbs, is both an accretional work and an anthology. It is a collection by genre rather than by theme, and so, unlike a modern book or anthology, it has no single author, editor, time, place or intent. The psalms were used in liturgy, private devotion, public celebration and other occasions where a short, memorable text that can be easily put to song is required. The oft repeated characterization of the Psalms as "the hymn-book of the Second Temple" is challenged in this article from the Christian Classics Ethereal Library.
Some of the other books of the Bible are also accretional (to varying degrees) and the entire corpus of the Bible is an accretional anthology. The characteristics of accretion and anthology of disparate and sometimes contradictory material are hallmarks of Jewish tradition as epitomized by the OT.