What exactly do you mean by a built in router? If you are referring to a wireless card that acts as a router then yes, there are some with that ability. I use an MSI wireless PCI card that can act as a wireless card, acces point, or gateway. Check the card you are buying to see if it offers such functionality. Understand though, that it will only operate when the host computer is on.
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You only need a Wireless card if the router you are buying has wireless capabilities.
Also you need a wireless card/adapter for any computer that you do not want to run a ethernet cable to from the router.
If you run a cable to the router you do not need a wireless card for that computer that is connected through the cable
What exactly do you mean by a built in router? If you are referring to a wireless card that acts as a router then yes, there are some with that ability. I use an MSI wireless PCI card that can act as a wireless card, acces point, or gateway. Check the card you are buying to see if it offers such functionality. Understand though, that it will only operate when the host computer is on.