As to the tying method I prefer, the choices are many and I am not sure what to do. What are your thoughts? Are there common traditions? Is it an issue of aesthetics or of religious belief or tradition? Any suggestions would be appreciated. I assume that they are all “kosher” knots depending upon the accepted authority? Which is the oldest known?

Concerning the choices, I have been asked this many times and have detailed the options on our site: http://www.tekhelet.net/diagrams/TyingFAQ.htm

If you would like a cut to the chase, I recommend Rambam strings tied according to the Rambam method as handed done by the Teimanim. There is an issue of aesthetics as one is supposed to have “beautiful tziztit” as part of the fulfillment of “zeh keli v’anveihu”. There is not really a tradition to speak of since tekhelet has been lost for 1300 years. All methods are kosher, that is they all fulfill the d’oraita requirements of a kesher elyon and three winds; furthermore, all methods fulfill the d’rabannan requirements, according to the particular posek’s understanding. Regarding the oldest known traditions, they are from R. Natroani (d. 730) [brought by Raavad], R. Amram Gaon (d.875), and R. Shmuel ben Hofni HaGaon (d.1034) [brought by Rambam].
– Mois Navon.