In my application I need to throw an exception if a property of a specific class is null or empty (in case it\'s a string). I\'m not sure what is the best exception to use
Well, it's not an argument, if you're referencing a property of a class. So, you shouldn't use ArgumentException or ArgumentNullException.
NullReferenceException would happen if you just leave things alone, so I assume that's not what you're looking for.
So, using ApplicationExeption or InvalidOperationException would probably be your best bet, making sure to give a meaningful string to describe the error.