It's difficult to say. There is still no reference on that page to the menu.css that that should be there (apart from the menu_ie.css).
The css for your new template is going to be quite a bit different from the css specially compiled for the store, and I think that as you get deeper into it, your problems are only going to get bigger.
But if you wanted to just change the basics of the menu (colour, font) then it might be safer to create a menu on a clean page, get it to look the way you want, and then copy just the stylesheet to your server (CSSMenuWriter/cssmw_home/menu.css ).
Bear in mind though that the styles were written to accommodate the structure (in a 1020px wrapper) as well as the look, so expect a few challenges later on!