Choosing someone to read something at your wedding should not be delegated to anyone who simply didn't make the wedding party cut. Make sure to choose someone is naturally extroverted, good in front of large groups of people, quickly adaptable, and is significant in your life. Often, ceremonies can have awkward and unplanned moments. The people who are speaking at your ceremony, whether it be an officiant or someone reading, should be able to adapt to a snafu with ease.
Make sure to acknowledge to those reading at your wedding that you consider the role very important, and that your relationship with them makes the reading that much more special!