Not familiar with IPcop but the best way to do this is as follows:
(1) Connect modem to IPcop red side and put the modem into Ethernet bridge mode. You will need to configure the WAN side of IPcop to have the IP settings from your Internet service provider if it is not able to pick them up automatically. Turn off the IPcop DHCP server and set static IP addresses on your workstations using a unique IP range... (for example, 192.168.0.* or 192.168.1.*). IPcop is a firewall and will do it's own routing. Put your Netgear router/AP on a fixed IP within the correct subnet and connect it to your LAN using one of it's LAN ports... NOT THE INTERNET PORT. This gives you access to full IPcop functionality and the Netgear becomes a wireless access point.
(2) Alternatively, connect the IPcop red zone to the modem and allow it to pick up a dynamic IP address from the modem. Assign static IPs to your workstations and the Netgear. Again, connect the Netgear using a LAN port NOT THE INTERNET PORT. In this config, the IPcop is shielded by the modem and you will not have access to full functionality. Your network is shielded by both the modem and the IPcop. The Netgear becomes a wireless access point.
In both configs, give the IPcop the external DNS server addresses and use it as a DNS proxy. Using it as a web proxy is up to yourself entirely.