" Will the same set up work with a pc(instead of the xbox), same wires? Could I get away with a cheaper router/modem? "
yes. With ADSL, any similar modem / router should be fine. £17 click here
" Also, my new pc has all the free broadband trials and stuff and I was wondering whether I need any of it?"
"Do I/Can I have a different isp?"
Yes, just use the ISP you use at the moment. Remove the existing modem settings.
Setup your ISP on the modem / router, with your details. Your settings on the Pc's are probably already setup. Should be just a case of connecting the lan cables and connecting to the net.