Make "Today" the default due date in a Task window
You can set your default values to automatically set your due date to today. Go to Preferences > Default Values.
The due date is when the task is due and the start date is when you start the task. You can have the start date automatically applied as well as a default value. That way it gets date and time stamped when you create the task. (this comes in handy when logging phone calls). Side note: The task will only show up on your calendar if it has a due date assigned.