that mentions an inbuilt ADSL modem in its description. There are many different routers made by companies such as Netgear, LinkSys, etc. and any model that suits your pocket will be fine.
Then you'll need to connect the router to a computer LAN socket to configure it. Any computer will do, it doesn't have to be your main PC - the cable connection is only temporary - while you set up and configure the router. Use your Dell laptop for that, it has a LAN socket.
Once that's done you can remove the cable (it will come with the router by the way) and use the internet wirelessly on any machine with range, provided it (the machine) has a wireless network adapter. Provided your PC has a spare USB port you don't need to open the case, you can simply use a USB wireless network adapter - there are many types, but Netgear or Belkin both make good ones.
Make sure you install the software for the adapter on your PC BEFORE you connect it to the USB port.
Once all that's done you'll be able to use the internet on either machine, without the need for the other one to be on.