Rule to fire only on first time publish of node
This is how I would try doing it:


create a field for the content type named first_publish, boolean, hidden, default value 0
create a Rule that when that content type is published, as a condition if first_publish is 0, first_publish becomes 1, add email output to user
create a second Rule that when the content type is published, as a condition if first_publish is 1, send out a different email


This will use a data field as a variable that follows the node - the rules will trigger appropriately depending on the conditions of whether or not the variable is set, giving different outcomes.