It's a bad idea to delete the Zen Cart stylesheet completely. You can't just apply your main site stylesheet, as its rules will be meaningless to Zen Cart's pages.
What you need to do is take all of your main site style rules and apply their property declarations to the appropriate Zen Cart equivalent elements.
And before you start doing anything, do not use the /classic/ folders for your custom template; create a new template following the instructions in the tutorials, and apply your customizations to that. All /classic/ files will be erased and replaced when you next upgrade to a new version.
picandnix - There is a complete ZC installation there, but with no stylesheet whatsoever.
The OP currently has a rudimentary shop in another subfolder.