If so, you can do that without any CSS. To disable commenting on all future posts and pages, go to settings > discussion and you can turn commenting and trackbacks off there.

For any existing posts or pages, you will need to turn the comments off manually, but you can do this with the bulk edit feature.

Bulk edit pages
Bulk edit posts

Since your site is private, I can't see it, so if this will not work for you, let us know.

I'd like to start by removing the 'leave a reply' box and would appreciate any advice on how to achieve this.

thanks,