I've not used joomla much before. I'm trying to just get one page of a site that uses a Joomla template to have a different logo than the rest of the site, or even hide it. I'm mostly a Wordpress developer, so just don't know how this can be done in Joomla.
Is there a way to assign a body class to one specific page in Joomla and have it hide the element?
If you edit a menu item, you want to look under "Advanced Options" and then "Page Display Options". There is a box for "Page Class" which adds a class to the page, so a body class as you wanted.
You can then tweak your template to show different pieces in CSS based on this class.
If you want to drastically alter the page, you can also assign different templates to different pages through the template manager. This takes a little more work (since you have to install and set up another template).
This would be the preferred way to handle a lot of changes so you don't have to have lots of competing CSS based on page classes.