If I buy Black/White 2 without having the originals, will I not understand the storyline?
I played B2W2 before B/W, and I understood pretty much everything in the storyline without the prior knowledge gained from B/W.
It's just that B/W gives some context and secondary meanings to things that you might not have known otherwise, e.g. why the Striaton City brothers are no longer gym leaders in B2W2 (via memory link), Cheren's back story which gives you insight to why he's become Gym Leader, why Bianca works as Juniper's assistant etc., but it's not essential or necessary to your game play.
I do recommend getting the originals first. Without them the game may be confusing.
No. You can get Black 2 and understand 90% of the story, easily