<p>If you have a Property that gets and sets to an instance variable then normally you always use the Property from outside that class to access it. </p>

<p>My question is should you also always do so within the class? I've always used the Property if there is one, even within the class, but would like to hear some arguments for and against as to which is the most correct and why. </p>

<p>Or is it just a matter of coding standards being used on the project?</p>

It depends on whether you want to apply any logic implemented within the property setter, and so you really have to decide on a case by case basis.
When you go directly to the private field, you know that the field is being set to exactly what you say.
When you go through the Property, the value gets set according to the setter logic, so you get any business rules or validation you want over values assigned to that field.
Pretty hard to come up with a rule about when doing either is 'correct', about the only one I'd say I follow is that in constructor initialisation I'd pretty much never use the Property.