Total number of published comments from the logged in user
You do not have to execute a rule every time a user submits a comment. If you have approved a comment for the user, then the permissions systems can handle it.

First create a new role 'Comments approved' and give the role a single permission to 'Publish comments without approval'.

Then create a rule triggered on the event 'After publishing a comment'. Have the rule perform the 'Add user role' action giving the comment author the Comments approved role.

This will mean that the user will be able to publish comments after you have approved their first one, and you will be able to remove the role from the user if they abuse the privilege.

If you want to get really fancy, create another role called 'Moderation only' with no additional permissions. If you have to control comments from a particular user, assign them this role, and in the conditions for the rule, check to see if they are a 'Moderation only' user, and do not assign the 'Comments approved' role if the 'Moderation only role' is present.