Being that you are starting from scratch as you posted, you should start with a template based on the template_default file set over the 2 stylesheet classic one that you are currently using. These things can be fixed with this template but at every corner you will be chasing things through the 2 stylesheets attempting to determine which one is causing what you don't want.

There are many threads about template_default that you can read

I don't know how many customers you have but would also copy the DB over so as not to lose their information,,,but this is your call.