I was just adding stuff to my test store to figure out how to kill those links, not work though. I can't replicate those links, I guess I already have them turned off. As usual, I can't remember how I did it. :wacko:
You could always do a search of the forum or experiment with the settings in Admin(that way, you can familiarize yourself with all the settings). That is if you get weary of those subcategory links.
I have to ask the dreadful question if you are using that classic template as is or if it's part of the template override system? If it's part of the overrides, then that's good. If it's not, I suggest for you to check out the 'downloads' here and browse around for a template to use. The Classic template will cause you grief with future upgrades. I'm just saying, because your store is new.