I've recently moved to a rented house - the only phone line is downstairs, my PC is upstairs. I'd like to go wireless, so I don't have the hazard of the modem cable stretching up the stairs, and so that I can use my laptop in the garden.

(The BBC gardening website, of course).
My understanding is that I need a Wireless router to plug into the phone line, and a Wireless network card for each computer. Is that correct?