Timesplitters 2 is where the actual story starts... more or less. If you've played Goldeneye, playing Timesplitters 1 will actually feel like a step back, despite being on a better system. Timesplitters 2, on the other hand, had better graphics and more reason for the story. Besides, the characters in the first one are fairly tame (for Timesplitters, calm down) and Timesplitters 2 is where the really wacked-out characters got their start.
Not much in Future Perfect will make sense unless you've played either of the first two. The story mode is fairly self-contained, I guess, but all the references and in-jokes will be so much funnier if you know the context behind them.