[insoluble]

> Turn off everything incoming except for HTTPS, SSH, and ping (optional).

OP mentioned using AWS, in which case Amazon's built-in "Security Groups" feature can be used for restricting access to the instance by port or possibly by protocol. Naturally, however, one would not want any dangerous outbound traffic, such as unencrypted/unauthenticated automatic updates, so there also is merit in controlling which services and programs are running.