If it helps with your design questions, here is how I have it setup here:
The IIS server is on the internal network, and is part of the Domain.
An ISA server sits on the Internet and the Internal domain, and functions as a publishing firewall.
The web server is published to the Internet through the ISA server.
Public (Internet) users can browse the website free of any login prompts.
Domain users can browse the website without logging in, and if desired they can click on one button and they are logged on using their domain account. Note: This will change once the next release comes out, which will allow us to use auto-login.