Questions have been raised about where to begin.
My suggestions will start with things that should already be familiar.
For narrative poetry--the Book of Job, and The Song of Songs (sort of).
For lyric poetry The Psalms.
There is a tendency not to remember that these are poetic forms. They are presented as poetry for a reason--for several reasons.
Poetry is usually more easily memorized than prose--it has hooks like rhythm or rhyme, which unfortunately, modern translations largely remove. But memorizability was an extremely important feature in an oral culture.
But the next time you set out to read the psalms, push the lines. Read them intentionally as poetry. Understand the line-breaks, understand the possible meanings that build up. Read them in several different versions and hear how different translators interpreted them. This is a critical factor so you can understand why some of us (me in particular) go on and on and on about the KJV or the circa 1660 BCP translations--or the Translations of the Countess of Pembroke , Mary Sidney. The language is older, and bit harder to slip into. But that's okay, it will slow you down, make you intentional in your reading. Poetry should be allowed to melt in the mouth like Neuhaus or Godiva--not chewed and swallowed like Hershey's. The savor of it should linger--but for that to happen it must be heard. As silly as you may feel about it, read what ever poetry you read aloud. Hear it, allow the words to sink in. The Liturgy of the Hours, properly done, should be vocalized, and at a minimum our mouths should form the words. There are good reasons for these rules--they slow us down. They force us to move at the speed of speaking rather than the speed of thought. More, they train our mouths to say words of praise, they train our minds to hear and recognize them.
Reading poetry should engage as many of the sense as possible.
(must run now--have the most unpoetic engagement you could possibly conceive of--I'll be back later to proofread revise, amend and perhaps post more.)
