I've never used a public proxy service, only the ones the various companies I've worked for made me use to get outside the company firewall. At least for those companies my Proxy settings looks similar to this:
I've specified the "Web Proxy Server" and port number (2 of the companies used 8080 as the port and one company used 80; it is all up to the way the proxy server is setup).
I've configured the proxy server information for:
"Web Proxy (HTTP)"
"Secure Web Proxy (HTTPS)"
"FTP Proxy"
"Streaming Proxy (RTSP)"
Gopher is so old, I'm surprised it is still listed, and SOCKS is really ONLY for a special kind of proxy server. The proxy server would specify if you needed to use SOCKS.
I have never worked for a company that required a username/password, so I do not have experience with that. However, I suppose if you were paying for a service, they might want to validate you are a paying customer via username/password.
"Bypass proxy settings for these Hosts & Domains" is default setup so that local traffic within your home local area network would NOT be sent to the proxy server. When I'm using proxies with the companies I've worked for, I've had to put things like company.com domain name (or names) in that list so that stuff that is inside the company firewall will not be sent to the proxy server.
I suppose you could put a list of domains in there for web sites where you do not want to get through the proxy server, but it could get very ugly very fast if you ONLY wanted to go to the proxy server for a small number of domains, and everything else was to not use the proxy server. The list would be huge, and unmanageable. If you needed that, it would be better to just create a separate network location with the proxy configured, and switch to that location when you wanted to use the proxy server, and then switch back to "Automatic" when you wanted normal non-proxy web access.
That is everything I know about proxy configuration.
If you are using a free public proxy service, you might provide a pointer to their web page and maybe someone would try it themselves to see if it was working OK for them, and then give you a screen shot for how they configured their proxy settings.
