Is there any way to play the original main Destiny storyline without Xbox Live Gold?
Solution 1:
Destiny is an online-only game (see the very first sentence of the Wikipedia article). You will need an internet connection to your Xbox at the minimum because you need to be connected to the Bungie servers. You can do this through an Xbox Live Silver membership. The big difference between Xbox Live Silver and Gold is that with Silver, you cannot play multiplayer (and it is free).