a lot of what you are trying to do may well depend on if you have a chipped xbox or not, if you are wanting to use a tunnelling application such as xlink Kai or if you want to go for xbox live.
If you are using xlink Kai
www.teamxlink.co.uk and a chipped xbox (this is perfectly legal as all it does is allows you to play system link games over the internet, not make illegal copies of games) set your xbox's IP to a static addres that will match the rest of your network, then set the NIC on your PC to a static IP address too. You should not need to bridge the connection, in fact if your wireless card does not support Promiscuous Mode then you will loose all network connectivity. What xlink Kai will do is automatically bridge the connection for you.
If you are wanting to use xbox live, you will find all the information you require from their website
www.xboxlive.com.
Either way you need a cross over cable you can get one of these from places like
www.aria.com