You don't "purchase" a wireless connection, except in the sense that you can walk into a coffee house and pay for internet access while downing a latte.
As you are on an ADSL - as opposed to cable - service, you simply need to purchase a modem/router. Do not make the common error of buying a router and trying to get it to work with your existing modem. With one or two exceptions, it's not supposed to work that way.
Your notebook will be wireless enabled, so that's that covered. I would need some confirmation from you about whether your desktop has an Ethernet LAN port; let me know so that I can advise you further.
A good router click here Ignore some of the customer reviews that refer to an early version; I own one and have purchased three for other people and it's a good router. Certainly one of the simplest to configure.