While the Yongnuo RF-603 (and -603II, and -605) and YN-560-TX units all come in Canon and Nikon flavors, the difference is solely for the "wake-up" feature (i.e., half-pressing your shutter button will wake up the remote flash if it's sleeping to conserve power). The Nikon and Canon TTL pin layouts are different, so the trigger "foot" used for the on-camera transmitter communication has to use the right pattern to communicate the non-sync signals. As long as you don't need the wake-up feature, then the sync compatibility and remote power/zoom control should be fine across all three brands. The hotshoe on the trigger used for communicating as a receiver to a flash is identical across both versions, with larger-sized contacts covering both patterns of pin/contact layout.
There are reports of the YN-560-TX working not only on Canon and Nikon (cross brands) but also on Fuji X, micro four-thirds, and the new Sony iso-compliant hotshoe.
Triggering-wise, you're probably better off getting the YN-560-TX to use as the on-camera transmitter unit because this will give you remote manual power and zoom control over the YN-560III flash with built-in receiver; the RF-60x units do not. If you also want on-camera flash at the same time, then a YN-560IV as the master unit is probably your best bet--but it only controls three groups vs. the YN-560-TX's six group control.
If you are going to go with the RF-603 or RF-605 triggers for cost/size/passthrough, then avoid the RF-603 (Mk I), and use the RF-603 Mk II. The first version of the RF-603s used a non-sync-pin signal to determine if the trigger was being used as an on-camera transmitter to auto-switch to the Tx mode. The problem is that signal is proprietary and different for most systems, and you would have to get one of each type (Canon or Nikon) to get an on-camera transmitter, and the unit will never be a transmitter on the Fuji X (or micro four-thirds, or Sony NEX) hotshoes, unless you feel like modding one. With the RF-603II, there's now an added OFF/TX/TRX mode switch, so you can explicitly set the unit to be a transmitter if you need to.
In addition, over the Mk I, the MkIIs also include a locking wheel (important if you're going to use the pass through hotshoe to keep the on-camera flash securely fastened), and the new OFF/TX/TRX switch is on the side of the unit where you can actually reach it with a flash mounted on top. The older RF-602 and 603 units have the ON/OFF switch placed on top, exactly where you can't reach it once a flash is mounted on top.
The RF-605s add an LCD screen, and group on/off capability.
The Cactus V6 triggers could let you remotely set the manual power level on a mix of Canon and Nikon TTL flashes, but cannot do anything other than fire Fuji X flashes in sync (manual-only triggering). You could also use the Cactus RF-60 speedlight, which works in that system the way the YN-560III works in the Yongnuo manual-triggering system. Most manual-only radio triggers will work with all of your cameras and flashes, but would not give you remote power control, and probably aren't built in to the flashes. So you not only have to remember to bring along the triggers, but also batteries for them.