How do I set up user's "Favorite Tags" and "Ignored Tags" tag subscriptions?
I would recommend using the Flag module to allow your users to pick "favorite tags".  It is still in beta for D7 however.  

Also, in the future you could look at the Flag Terms module to allow your users to flag taxonomy terms.  That module is still in dev.

You can use Views to create lists of "favorite tags", etc.