MacOS – Setting proxy settings to “Auto Proxy Detection” using the command line in macOS

See this Wikipedia page on WPAD for how proxy autodetection works. Remember, DHCP based WPAD does not work in Firefox.

In your case you'd probably want to use Automatic proxy configuration URL. PAC files can check which subnet you are on (e.g. 192.168.1.x vs 192.168.2.x vs 10.5.x.x, etc), so if the home network uses a subnet unique to other networks you connect to, this will work. More information here.

Basic check for subnet you are in (taken from last link):

function FindProxyForURL(url, host)
{
    if (isInNet(myIpAddress(), "192.168.1.0", "255.255.255.0"))
        return "PROXY 192.168.1.1:8080";
    else
        return "DIRECT";
}

Simply edit your /etc/profile file with ie, nano:

sudo nano /etc/profile

and at the end of the file add

http_proxy="http://user:password@foo_server:port"
https_proxy="http://user:password@foo_server:port"
ftp_proxy="http://user:password@foo_server:port"
export http_proxy ftp_proxy https_proxy

where foo_server is your proxy server, and port is the port you need to connect to your proxy server.

To check if the new settings are in use simple use type source /etc/profile and you can then check that the server is in use with (install curl if you don't have it yet)

curl icanhazip.com

that should return your proxy server's address.

Software like git, ssh, telnet, will tend to ignore those settings and use their own, I know that there are several utilities for ssh that allow you to do that. There wont be a unique, works for all way of doing it.

Maybe separate questions, regarding each service you want to use is a better option than asking for a global way of making it work, the short answer here would be: there is no global way.