Q: How can I easily create a visually appealing Home Page that displays modules in a non-linear way?

A: One can set the Module View to Tile View instead of the default Standard View. Do this via Settings > Configure Module View. Toggle the switch from Standard View to Tile View.

Further information is available on the page: Course Presentation and Navigation tool.

If your Home Page has been set up to display Modules, the Tile View will display all existing modules on the Home Page in a two-dimensional layout, with a coloured box for each module. It will also display a sub-menu of the module structure on the course navigation menu. When you are within a module, it will show a small icon per page, to facilitate navigation between module pages.
If your Home Page is set up to display a Canvas page, it will not be replaced by the Tile View, but the additional features mentioned above will be enabled.