Quote: Is it possible for my 'host' PC to stay how it is, recieving the Internet directly from the USB modem, but it has something similar to a router plugged into a spare USB slot...which then sends the signals to other PCs with wireless cards etc.?
Put simply no.
You need an modem with an cat5/ cat6 output. The connects to a router's WAN interface. You can use another cat5/cat6 cable to connect the router's one of the LAN ports to the host pc. Then you need to buy a wireless bridge for the xbox and the other pc, that will connect to your router's wireless interface.
You will need to buy a router that has a wireless AP built-in. Make sure all the cables are straight though cables.
That is the best configuration for your situation. You need your ISP to give a modem with a cat5/cat6 output build-in. Don't buy a router with modem's built in as those tend to be troublesome to setup.