A lot of state poetry societies have contests with small entry fees -- a good place to get your feet wet. Many of them have specialized categories (i.e. haiku about animals, or sonnets set in space) which gives you more specificity and possibly a greater chance at winning, if your poem happens to fit that category's criteria. These contests often have entry fees of just a few dollars (even less if you're a member of the state poetry society).

Here are just a couple:

- Missouri State Poetry Society Winter Contest 2017
- Illinois State Poetry Society Poetry Contest
- Utah State Poetry Society Contest
- National Federation of State Poetry Societies Annual Contests