I find that when people write poems, there's a certain cadence to the words.
Then when they try to fit it to a 4/4 or 3/4 beat, they change the cadence of the words to force it to fit in.
It often does not work out very well.
I think a great way to start is to simply get a metronome out and get a tempo established.
Then just start singing your poem.
Once you have a melody you like over a tempo you like, figuring out the appropriate chords should be pretty intuitive.