I'm in Southwest MO and work for a private, non-profit adoption agency. I also used to work for DFS as a social worker back in the day. I think cost can vary widely. If you are thinking about adopting through the state, the cost would be fairly minimal, start out by contacting the DFS office in your county and talk to the worker who does the foster care licensing and let them know what you are thinking about. If you want to know more about the agency I work for, I would be happy to give you some info, just pm me.
Good luck on your journey, I've loved working with families from all sides of the coin.