You'll have no problem with using that kit on your BT basic package. It seems like the best way of going about doing it. As long as the wireless router has an ADSL modem built in and is not packaged as a "broadband router" then it will be as simple as entering your BT username and account into the router and off you go.

Personally I would get a USB instead of PCI wireless card because you can posiiton it more easily for a strongest signal. The only other warning Iwould give is that if you play online games a lot you'll find your latency suffers as a result. Oh and don't forget to turn WEP on so that your neighbours don't use your broadband for free.