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For a PC you would use either PCI or USB; for a laptop either PCMCIA or USB.
<<< and cable/dsl router to connect my laptop to the world wide web. >>>
To connect with a Wireless Network adapter, it needs to be a *Wireless* router. Cable broadband (NTL or Telewest) uses a "Cable/DSL Router. ADSL via the phone line requires a combined "Wireless Router/ADSL Modem".