Davey,
There are a few different ways to stream to your TV. For amazon prime, the Firestick works really good. Just plug it into an HDMI port on your TV.
HDMI cable from computer to TV was the way we would watch the NCHC hockey games until I found that Apple made an adapter going straight from iPad to HDMI. That is slick and a better feed.
If you have an iPad, get the Amazon Prime Video app. It allows you to stream shows with wifi but also allows you to download the show and watch without a wifi connection. I usually have a couple episodes downloaded to kill time when waiting to pick up kids from their various activities. Then just delete off the iPad when watched. And if you didn't want the Firestick, you could use the adapter and stream right to your TV from iPad.
ek