When I try to add new sites, it adds them, but I can't access the default index.html page by typing in the domain name. My guess is that it is giving new sites a private IP instead of a public one. I'm new at this, so please ask for any configs or logs you require
That's really unlikely. By default, ISPConfig is using no IP, it uses * instead of an IP and you should select * in the website settings. The more likely reason is a problem in your dns or router setup.
Could you help me out on how to diagnose this? What could this possibly be and how would I check if it's that? Thanks for your quick reply
Have you selected * in the ipv4 field of that site? Did you add the site as domain example.com and is auto subdomain www active?