Final answer:
A while loop is best for programming tasks that require iteration with exceptions, as it can be controlled using complex conditions.
Step-by-step explanation:
When addressing a client's programming needs that involve iteration with certain exceptions, the most suitable type of loop to use would be a while loop. A while loop is ideal because it can iterate over a block of code as long as a specified condition is true, and it allows for complex conditions and exceptions. For instance, it can run a task repeatedly until a particular condition is no longer met, which could represent the exception to not performing the task. In contrast, a for loop is generally used when the number of iterations is known beforehand. The options 'then loop' and 'if loop' are not standard loop constructs in programming.