Odds of Getting In
Becoming a full-fledged, honest-to-goodness successful writer with a poetry-based income is extremely difficult—in case we haven't driven that idea home by now. In order to get to that point, you'll have to write thousands of poems, submit to hundreds of literary magazines, and publish dozens of collections. And even then, people have to actually like what you've written.
If all you want to do is get published, your goal will be a bit easier to achieve—although it's still no cakewalk. Many publishers will only agree to put out your collection if you've been published before, either in a prominent literary magazine or through a first book prize. That's right, to get published you need to have been published. Thankfully, irony's a fairly decent poetic device.