If 127.0.0.1 (localhost) works, that means Filezilla is set up correctly. To be accessible, you need to open port 21 (TCP). The admin interface runs on a separate port (I think its 14141 or something like that), but since you generally only run that locally, you don't need to open any ports for that.
I have a similar setup:
DSL Gateway -->
-3 Computers wired
-2 Computers wireless
-Router -->
--2 Computers
I solved the double routing/firewall problem by setting my router to run in bridged mode (this essentially extends the ports on my DSL gateway (which is a wired router, modem, and wireless router in one) and lets it do all the routing, turning the router into a switch. This allows all port forwarding to be setup through the DSL gateway. I'm not sure if you have the capability to do that on your modem or not. But it simplifies things a bit if you can.
In order to get the forwarding capability to function properly, you only should have port 21 opened on one IP, the IP of your server. All others should remain closed. You should then be able to access your FTP server by punching in the name of your server (for instance ftpserver) in your FTP client as the address. Alternatively, you can use your servers IP address (192.168.1.105 or whatever it is). To view in a browser, just add ftp:// to the front.
Also make sure Windows Firewall isn't interfering. If you have everything set up correctly, you should at least be able to access the FTP server from within your LAN. Some ISP's block common ports (like port 21, port 25, port 80) for tighter security and to prevent the spread of worms. But this shouldn't effect your LAN.