Many routers have an option to open up NAT for one single device while forcing NAT for any other devices.
NAT is good to have running because it goes a long way to help protect the computers behind your router by giving them a 'fake' local IP address that is generally not discoverable to others out on the Internet. This is the part that often messes up gaming systems that like to have a real internet based IP.
I'm betting that your router will allow you to assign a real internet address to the 360 box and you can leave the rest behind NAT. You will need to be able to identify what the MAC address on your 360 is. I don't have a 360 but it probably tells you this info somewhere in its network setup screens.
UPnP is usually your safest bet but if you can turn NAT off altogether for the 360 then that takes it out of the picture altogether. It leaves your 360 more exposed to the internet but it doesn't really need to be protected as much as your PC.
