It's not something that you need to play the first Bioshock to understand. Quite the opposite. I've found that this game serves more as a prequel, where if you played this first it would probably help you follow the Bioshock plot better.
Perhaps saying they were in no way connected was going too far, but nothing that happens in the first Bioshock game is directly translated to this one. It's the other way around, this game takes place 40 years earlier, so it's Infinite that translates to the first game.
It's a prequel, not a sequel. The first Bioshock hasn't happened yet, so nothing that happens in it effects this game.
I am interested in hearing your thoughts on the ending. Please let us know what you thought of it when you finish the game.
I personally think everyone needs to play the original Bioshock to fully appreciate this game.