That is quite a lot of information, most of which is covered reasonably well in the documentation. The list is quite long, but apart from the helpfile you can find useful information for basic setup
here, ADSL
here, public and private IPs
here, TCP/IP properties for 2000, XP and 2003
here . A brief overview, however:
1. First, ensure that you have a private IP on the Network Card that will connect you to the other computer.
2. Install WinGate on the machine with the internet connection. Keep all default settings for now.
3. Follow the login instructions (In the helpfile). Once you've done that, switch to the "Networking" page and check that your adapters are marked properly. The Network card connecting to the ADSL modem/router should be marked as "External" while the Network card connecting to the other computer should be marked as "Internal".
4. On the client computer, open TCP/IP properties and set it to "Obtain IP address automatically" and "Obtain DNS/Name Server automatically". That way, WinGate will allocate an IP in the internal range to that machine and because of DHCP it will be configured for NAT already.
The machine should now have internet access, your ADSL connection should be properly firewalled and everything should still function as normal. Once you've reached that stage and have the internet connection successfully shared we can fine-tune the installation to meet your other requirements.