Using a state agency might be the best bet to actually get the child support. It might be awarded a little faster. It is completely up to you though, file the way you want. Maybe you should consult with a lawyer.
First,id talk with a lawyer. But also do what you feel is better for you, and the child. Personally, id file with the state agency, its free, faster, and they make sure the other party pays whatever they owe you.