Do you need a desktop computer to hook up a wireless router?

You will always need a service TO your wireless router, either a separate modem or a built-in (modem-router). However, no reason that you can't use wireless to a desktop - wired would probably be more dependable though. If the desktop doesn't already have wireless capability, it can be added by a USB Wifi adapter, or maybe an internal card, PCI or PCI-E as required, would have lower CPU overheads.

If Wifi was my permanent desktop connection, I'd want it as a card, not taking up a USB port.

You will always have to pay your internet bill if you want to have internet, wireless or not you need the internet connection, you can connect a desktop to a router using either an ethernet cable or by using a wireless adapter on the pc to give it wireless capability, you need to keep the modem to connect the router to it, then connect the pc to the router by either ethernet or wifi. You can get a usb wireless adapter to fit on the pc, these are the cheapest and easiest option.

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