TL;DR - In the Package Manager Configuration, turn "Auto Update" OFF and make sure 1.3 is the selected version. Then, manually add the TV Extensions 3.0 repository to the Extensions SDK.
Why would you want to build apps for Fire TV? Well, Roku may be the current leader in the market for streaming TV boxes, but Amazon Fire TV's share of the market isn't too far behind at 2nd place based on data collected from comScore as of December 2016. And like other Amazon Fire OS devices, Fire TV is built on top of Android, so we can leverage most of the existing Android libraries and tools to build our TV apps, making them useable on both Fire TV and Android TV devices!
If you've used a lot of Fire TV apps before, you may have noticed many of them have a very similar look-and-feel. This is because many (if not all) of them have built their apps on top of the Android Leanback support library, so they usually end up looking similar to this out-of-the-box design: