Expansion and felxibility
I'd use the router and just share the connections with the internal machines if all you want is web access.
If you want to do some fun things like run a WebServer, FTP server, etc. you might think about using the Linux box as your first firewall then with a 2nd nic in the linux box feed the router's WAN port and route to your internal network.
You wouldn't need to do it this way to run a web server if your router allows you to forward ports, but it's the way I've got my home setup done. I did it this way for low latency. I run a game server (Counter-Strike) on my external Linux box and any device between it and the internet adds presious ms to the latency.
Again, if all you want to do is share internet access, just use the router. It's a lot easier in most cases.
MrKnisely
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