Based on my experience with the same process, I would apply to both Federal District and Circuit judges. Your class rank and position on law review will make you a competitive candidate. However, that fact is that you will be competing for clerkships, especially circuit ones, with students from T14 schools with your same credentials. Thus, it will be important to apply to plenty of district judges. The most competitive circuits are DC, 2nd, 7th, 9th and those in big cities. Similarly, district clerkships in NY, SF, Chicago, DC, etc. are more competitive than in Fargo, Salem, etc.
I have not heard that a published note is requisite. Most judges ask for a writing sample as part of the application and I believe that they often do not want a completely vetted work product because they want to see your individual writing without outside editing. Finally, strong letters of rec are vital to securing the most competitive clerkships.
Good luck. I'm still trying to decide whether or not to apply.