I never quite finished X3, but I bought the X3 SuperPack (or MegaBox or UltraCube or whatever it's called) that included Terran Conflict, and so when Albion Prelude came out I got that for free as well.
Trying to play X3 and then both expansions seems like it would take more time than I have on hand, but I think that they fixed many of the annoyances of the original X3 in the expansions, so I kind of want to play through at least Albion Prelude.
Is there a cohesive story arc between the game and its 2 expansions? Is there anything I'm missing out on if I jump right in to Albion Prelude? Are there any other requirements before I start Albion Prelude that would make it so that I have to play the others first?