Sebastian,
The 5 traditions (den) of Koto are Yamato, Yamashiro, Bizen, Soshu, & Mino. Each of these had sub divisions. Once Shinto came around the lines between the traditions blurred and the smiths of this time and later are said, in some cases, to work in the style of one of the 5 Den, but not to be of that Den. There were many different schools in Shinto and later.
I think there is a list of recommended reading at the links at the top of the NMB welcome page (or somewhere here). Read every book you can get your hands on, and if you learned something read them again.
Grey