If you want to use TTL exposure measurement, you'll need to stick to a Fuji or Fuji-compatible flash unit (i.e. one made by another manufacturer, but specifically designed to work with Fuji.) TTL flash units designed for other brands won't work, even if the physical locations of the contact pins match up, because there's no standardization among manufacturers about how the camera and flash unit communicate.
You CAN use other brands of cable, because the cable just carries the signals between the camera and flash. You just need to make sure that the cable's contacts line up with those on the flash unit and camera. Watch out, though -- even if the contact positions look the same, they may not be exact enough, or may require wiggling and jiggling to get them to work.
Or if you don't care about TTL exposure measurement, you can buy an inexpensive "non-dedicated" flash with strictly manual controls. Look for one that has a single signal pin in the center of the mounting "foot" -- this assures that you're getting a pure manual unit, and should work with almost any off-camera cable. Starting with a fully manual unit is actually the best way to learn how flash really works: its effect on the picture will depend only on its distance and power setting, so you can count on getting consistent results as you experiment.