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1) You will normally get the ntl250 modem The modem has an ethernet (RJ45) port. It supports only one direct connected device at once, i.e. a single computer, or a router. When swapping the connected device you must power down the modem or it will not recongnise the change.
2) 12 months contract after which you can cancel with 30 days notice (phone ntl:telewest, give your excuses and await the retentions team trying to keep you on - follow up any cancellation by confirmation in writing to guard against odd "computer doesn't do what it's been told" issues).
3) Many people have got on well with the Linksys WRT54G series routers. But Netgear and Belkin do so to. You may need to experiment with the channel settings. Try to place the router in a central location, reasonably high, and not in a corner of a room for best service. There are ways of setting up booster stations, if you find signals are too poor
4) Yes it is unlimited use (no caps). However traffic shaping is a real possibility, especially if you are using p2p type applications.