Any internet will do that has sufficient speed, and depending upon what else you at doing simultaneously would suggest a bar minimum of 5mbps, but at least 15 mbps. In terms of the stick, the stick is ok for content off of netflix/Amazon, but is not well suited for other streaming services like direct tv now, just does not have the horsepower. If budget and space allows would steer you to a "puck" style device as they have more oomph.
The speed of your internet and distance from router may affect performance. So if you see a lot of buffering or failures to connect, check those before assuming the Stick is faulty.
Any internet.
Fios is just Verizon's copyrighted term for their Fiber-optic wifi network. Wifi from any service provider will allow your fire stick to connect to the internet.
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