First off,

to the site. To try to answer your questions,
1) You do not need anything specific to NTL. you need a router with an Ethernet WAN port (NOT an ADSL modem/router with an RJ11 port).
2) The router connects to the cable modem via the ethernet (rj45) WAN port. What I'm not sure about, is how/whether the PC can connect to the router via USB, Someone else may be abe to answer that. If you get a wireless router, you won't need anything extra on the lap-top.
3) I'll leave this to others. I use a Belkin wireless router, but the favourite on here seems to be Linksys.