Installing a digital certificate from a trusted certificate authority on the server is the most critical step for securing communications between a client and a server. This allows for the use of SSL/TLS, which ensures the authenticity and integrity of the data. Self-signed certificates may also encrypt the communication, but they do not provide the same level of trust as they might not be accepted by users' browsers without creating security exceptions. Renewing existing certificates is important, but only applicable if the certificates are near expiration or compromised. Generating a new public-private key pair is a part of the process but without certificate issuance, it doesn't ensure secure communications.