hi
The point of using a router is that it 'pretends' to have only one IP that Telewest can see, while handling the switching of the correct packets to the client computers.
Usual advice is to set things up wired, before trying it wireless & the default setup should work (obtain IP automatically, DHCP server enabled). Mac/PC isn't an issue, as the router just sees them as network devices.
I'm surprised you think the modem is 'flakey' because it has to be power cycled after making changes - it is necessary to reset the internal memory, not a fault.
After making any changes, the routine should be turn everything off, switch on the modem, wait for it to stabilise, switch on the router, wait for it to stabilise, then switch on the client computers, which should both get assigned an 'internal' IP. You can't 'hot plug' devices into the router, so any 'new' device should be switched off when you plug it in, switching it on should then get it an IP assigned.
Wireless is another ball game, which I can't help with, though