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Yes the best bet is to use a router, that way each computer can operate independently without others needing to be on.
Most ADSL routers will not work correctly, as they have an ADSL modem inextricably linked to the WAN port of the router. Recommendations for routers that will do the job are in this article:
http://www.cableforum.co.uk/board/article.php?a=74
You need to be using ethernet from the cable modem (if that is how you are supplied) rather than USB connections.