Final answer:
To transmit confidential data securely on a public wireless network, the most effective method is employing a VPN, as it encrypts the data in transit.
Step-by-step explanation:
Under the given options, a public wireless network can be used to transmit confidential data most securely when C) The local computer connects to the network using VPN. A VPN, or Virtual Private Network, encrypts data transmitted between the local computer and the internet, safeguarding the information against potential interceptors. Though having an updated operating system, a virus-free computer, backed up files, and a strong network password contribute to security, they do not directly protect data in transit over a public network in the same way a VPN does.