Having only just bought the game and not played it, I would hesitate to say you should enter the Drakengard franchise because of Nier. The connections are great, yeah, but Drakengard 1 and 2 were varying degrees of terrible. The only situation where you need to get Drakengard 3 is if you, like me, really really love the first game for some god forsaken reason, and need to know. But it's not going to be Nier 2, if that's what you're really looking for. That said, if you haven't played Drakengard 1, there's an excellent let's play of it on the Let's Play Archive by the Dark Id. It's text and screenshot, but it's one of my favorite let's plays of all time. I'd say look into that, and then decide if you want to a part of this awful family.
Do not pay any mind to Drakengard 2. It's an awful game with none of the interesting things that Drakengard 1 had going for it and all of the terrible everything. Avoid it. Besides, if you take Nier to be the true sequel, like I do, then it's not even canon, and let it remain that way.