You can file with the state of Missouri for an administrative order that would require him to pay child support and possibly provide health insurance for the child. These administrative orders do not deal with custody or visitation. You do not have to hire a lawyer for the administrative order, and the state does not charge you for these orders.
If he wants to get visitation, he would have to file a paternity/custody action with the courts. You would have the right to participate in the court proceeding and have input on the terms of visitation. The court would also deal with child support.