A:Answer It sounds like you have Wi-Fi and Blue Tooth confused. Lets start with you router question.
The price goes up as the routers get faster. You need a router that is fast enough to do everything you want to do. If you stream video, like using Netflix, you need a fast one. You will find "N" routers and "AC" routers. AC is faster.
Blue Tooth is how two devices talk to each other. For example, your cell phone playing music over you stereo. I have a Fitbit too. I sync it with my IPhone and IPad. No internet is needed because they communicate using Bluetooth.
Hope that helps.