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I'll echo what Kirivon said:
If you're doing "studio" lighting, using manual flash adjustments is the way to go, and walking over to your lights to change the output isn't usually a major problem; once you have them set you may do several shots at the same level, just changing the pose and such.
Using inexpensive radio links like the RF-602 or options from Phottix is a good way to get started.
If you're doing fast-paced location work, where you need ETTL or remote-manual control, then ETTL-capable radios are the best way to go; but they're a leap up in price.
If you have the 5D Mark III, then I'd suggest getting the new 600EX-RT for off-camera flash, and the new ST-E3 radio transmitter for the camera. By the time you factor in the cost of new a transmitter, a receiver, and -- in the case of Pocket Wizard -- the RF shields, going with the new Canon gear won't be the much different cost-wise, but the convenience factor of everything being designed from square one to work together will be great.
You can still use your 580EX II in either Manual or with the built-in Auto Flash sensor, and trigger it from the flash of the 600EX-RT as long as you're not using the latter in ETTL. (The preflash for exposure calculation would prematurely trigger the 580EX.) You'd only need to attach an inexpensive optical trigger to the 580EX II.
Here's one that's compatible with Canon flashes (most aren't):
This one is handy because it has an 18-inch long cord so that you can aim the sensor at the triggering flash, while the triggered flash is in a soft box, around a corner, behind a scrim, etc.