Borderlands 2 does not require you to know the story of Borderlands. However, BL2 WILL exploit and even retcon some events of BL1, so the plot is certainly better if you DID play BL1. But noone plays Borderlands for the plot, really, and the plot was actually non-existent in BL1 (even though BL2 wants to make you think otherwise). So yeah, while the story is better if you did play BL1, it is not required to do so at all.
I really recommend you to get it, but I am the guy with a Borderlands nickname and avatar soooo... anyway, yeah. You should grab it. You should also look up the Psycho and Mechromancer DLC characters before you start the game. See if they interest you and buy them if they do. I personally think that Krieg (the Psycho) is the most fun character in the game, really fun to play as.
Also, you can probably ignore the season pass DLC unless you plan to play the game a LOT. I only really recommend them if you plan to keep playing the game for a while, instead of just doing a first playthrough and stopping.