I forgot to mention I hate getting in to sequels first. I have to start from the beginning
I'm the same way, but Arkham City has pretty much nothing to do with Arkham Asylum other than that it's another Batman game by the same team.
If you are saying you haven't played the first Bioshock and therefore can't play Infinite, what's wrong with you? Bioshock is a must play. Play that one instead. ;)
Farcry 3 has nothing to do with Farcry 1 or 2. It's a standalone story. Same with GTA V.
I've never played any of the Killzone games, but I've heard they are pretty good FPS's. No idea how important the plot is.
I haven't beaten Borderlands 2, but they sum up the extremely shallow plot of the first game in the intro.
Regardless, just do what Mr Gardoki said and watch some Youtube summary videos. The way sequels are so common now days, you'll end up hardly playing anything if you are dead set on playing every previous game in a series.