Great tip, @Danielle-GenD! I have now created a Status custom field in My Tasks with your suggestions of Started, Incomplete, Awaiting More Info and Not Started.
I added functionality to to this by taking a tip from @Bastien_Siebman, and adding actions (via Rules) to my new Status custom field. When I complete a task in my to-do, I update the status to complete using a rule. As I add additional status options, I will build in actions that do all sorts of things.