Hello Jon,
You should upload your index page inside public_html. /home is the home directory of the server and your home directory is inside /home with your username.
You can access your
website hosting temporarily using http:// 87.117.234.180/~username/ but not with the IP directly as this IP address is the shared IP of the server and its default root points to index page of cpanel page.
For FTP you can use the IP address but dont specify any directory while setting up connection. You can manually browse into the public_html directory and upload your contents in it.