If a PDA has "built in Wi-Fi" do you need an additional router?

Yes, the WiFi will only work if you are connected to a wireless network. Otherwise it will use the cellular signal to connect to the Internet. If you only plan on doing occasional browsing then the WiFi won't be of HUGE benefit to you. But again, you will need to be in the range of a wireless network in order to get the speed boost from using the WiFi connection.