I use a router, simply because it is easy to connect my laptop, smartphone, pcs, internet tv and log my visitors in to it when necessary.
But the wired adapter is quicker and more secure. However, most if not all wireless routers have ethernet ports too, so you can quickly plug your laptop in if you are worried about security when using internet banking and so on.
As you have a desktop pc I would really settle for the router with the pc connected by ethernet and the laptop connected via wifi.