I literally just finished the game, and it was awesome. The game increases the quality and amount of the anxiety filling "scary" moments. They introduce many new characters with qualities that make it easy to both hate and love them. Something I noticed a lot was the use of beautiful moments that connected us to the characters and the story. For example in the first game (spoiler alert) when Joel and Ellie see the Giraffes, it becomes this beautiful moment that fans loved and i loved. It was an escape from the horror aspect we are all used to.
Those moments occur more often in the game. As for following the story of the first game, Last of Us 2 does not do full justice as many fans would have liked. But you can't always have it the way you want. I would say buy this game if you loved the first one. If you're still not sure, well than you can always wait until it goes on sale on the app store or at a store.