Sorry that you are having this problem....search this site for what I am about to suggest as there are many posts that say about the same thing. I know that this will be frustrating as you already have a start that you sorta like, but it will be the best course forward.
You are using the 'classic' set and this is really not recommended for many reasons;
One is that this will cause you many problems now and when future Zencart upgrades become available. It is included only to ease upgrading for previous versions.
The combination of the css files in this make for difficulty in controlling what you are doing. Some of it is caused by the inclusion of tables and some by the order the multiple style sheets are processed.
As you are setting this up fresh, I would bite the bullet now and avoid future problems by deleting the contents of the /templates/classic folder, leaving the empty folder there. This will force the use of the template_default. Then you can create an override folder in /includes/templates/your_template_name. Copy the template_info.php file to your pc and edit the template name to what you like and upload it to your /includes/templates/your_template_name folder. also create the folder structure as you require it for those files that you need to alter. i.e. for starters you will need the css folder from template_default copied to your template folder with the files contained as you will be editing the css files.
You should search the posts and the area for how to use the override system as this is crucial to your having easy success with this cart.
From there you will be setup to use the power of css and ZenCart without the complications of the older tabled version.
There is a free template to begin with if the template default & css is too overwhelming for you. It is available here in the contributions section as future Zen template.