How do I run a web server behind a router behind a cable modem?
Your setup sounds a little confusing but you're on the right track. Normally you would configure your internet router (the one that receives its IP address from the ISP) to forward port 80 (http) inbound (port forwarding). Then use DDNS so people on the Internet can hit your server. You should put a DDNS client on the server if your router won't support it. The client checks in with the DDNS service periodically so that it can update your IP address if it changes. You may also want to forward port 443 for https.
Also make sure your 'upstream' speed is fast enough to support a server. Loading web pages doesn't take that much bandwidth I reckon but downloads on a slow pipe would be annoying.