Thinking of getting the 3rd game, but 90% of the reason I play a game is to get involved in the story. Is the story disconnected or should I know something before embarking on this adventure?

extremely seldom, there is a remark about something from game 1 or 2 but you won't rly miss anything storywise if you start with 3.

You can play each part as a standalone. But you can carry characters and items from part 1 all the way to part 3. If you are involved in the pen & paper game behind the series you most likely already know the connection to its metaplot. If you are not, you most likely won't care anyways. But if you care about it: It's connected to one of the most important campaigns in the Realms of Arkania