Firstly, if this is your personal machine, there is no need for sudo.
You can su - to perform administrative tasks. The point of this, is so that you don't accidentally do something stupid (ask anyone who has used unix for a while - you'll get a story
By using sudo, you are bypassing that restriction, allowing you do make a mistake when you are not root, and that is a bad idea.
Your visudo syntax is correct, however, I think you misunderstand how it works. Sudo by itself does nothing for you. If you wanted to configure an interface, for example, you would type:
The sudo command requires a command that you would like to run right afterward. It will parse /etc/sudoers, and make sure you have the permission to run that command.
Try it again - sudo init
You should get a usage prompt.