Don’t be so quick to blame yourself. Setting up WP shouldn’t be that tricky or difficult. Surprising incompatibilities do occur.
That “something’s gone wrong” error shows up when a customizer script is unable to save settings through the API for some unknown reason. Expected problems like not logged in or a bad nonce are handled separately, the API is responding with something unexpected when this error shows up. I think some sort of security is being applied when it shouldn’t be. Like one that prevents cross site scripting (XSS) for example. Not that XSS security is the problem, just that it’s something along similar lines. Mod_security for example. It may not be WP after all even though it appears to be on first glance.
Allowing that it could be WP anyway, I’m always leery of host provided one click installs through cPanel. If it were me in your position, after making a full backup of everything, I would obtain a fresh WP download zip from www.ads-software.com and use it as the source for a manual update. Essentially wiping out the host version for a true default WP installation.
There is a chance that a true default installation is incompatible with some odd server configuration implemented by the host, hence their modified one-click install version. My suggestion could cause more problems instead of fixing the other. If that happens, restore the original files from backup.
If a manual update simply results in the exact same problem, I suspect some sort of server level security preventing proper API access by customizer scripts. Your host could confirm if anything like this is in place.