If you are swapping out your old router with a new one, just plug one of your wired PC's into the new one and configure it to use the same IP address as your old one had.(If the factory set IP address of the new router is different to your old one, browse from your PC to that IP address and then change it within the router configuration menus).
If you were using WEP or WPA on your old router, make sure you set up the new router's WEP/WPA with the same network key as the old one had.
This way you shouldn't have to change any network or firewall settings on any of your PC's.
NOTE: It you had restricted wireless access to specific MAC addresses on your old router, this will need to be done again on the new one.