Hi
You did not say exactly what you mean by "not working" so I'm guessing you are faced with 404 generated by your web server when trying to load any page other than the home page. If different, please describe what happens exactly.
If you get 404s from your webserver (ie not the Joomla or sh404SEF error page), it means you have not set up a proper .htaccess file on that private server.
I'm wondering if you know of any settings I need to configure to get it working
Not sure you're asking about configuring sh404SEF or configuring your web server. There's no need to configure sh404SEF - or Joomla for that matter, the problem is a web server configuration, namely the missing or misconfigured .htaccess file.
I can't really help you with the content of the file as it depends on your specific server installation and configuration, but usually starting with Joomla default .htaccess is fine. Joomla has a detailed documentation page on how to do this and a step by step description of the process.
You can actually disable sh404SEF while doing the server setup (set "Enable URL optimization" to "No"), to have less moving parts. Once you have the server URL rewriting working with Joomla SEF URLs, you can enable back sh404SEF and it will work just lke Joomla - because URL rewriting is done by the web server, not by or inside of Joomla.
Best regards
Yannick Gaultier
weeblr.com / @weeblr