What proof or evidence do I bring to court with me?

You can bring whatever witnesses, documents, and other evidence you think support your case. It may be helpful to read the rules regarding evidence for your case type.
Resources:
•    Justice Court Rules of Civil Procedure
•    Arizona Court Rules
•    Rules of Evidence in Courts in the State of Arizona
•    Rules of Family Law Procedure
•    Marital and Domestic Relations A.R.S. Title 25