Gear-wise, the list is pretty simple. You need a flash and a way to trigger it remotely and a way to control the power output of the flash. This typically means a flash with manual power control and cheap radio triggers of some kind.
This will then be followed by a need to position the flash where/how you want it and some type of diffuser, which leads to a stand, umbrella swivel, and an umbrella. However, of these three pieces, the swivel (and its stud) is actually the most important. You can attach a flash to anything with a 1/4"x20 thread (like say, a tripod, or a clamp with a bolt attached) if you have a stud and a swivel.
If you've NEVER used flash at all before, and you're really starting from ground zero, here's my advice: start with on-camera flash. Start with bouncing. Start with an OEM flash that's got TTL capability (you can use it just as easily off camera in M mode, too). It's much much much easier to master the basics of flash if you're a) using only one, and b) not worried about getting a whole bunch of other gear. Amazing things can be done with an on-camera flash and a $1 piece of craft foam. Go read Neil van Niekerk's Tangents blog as well as the Strobist. There are times to haul an extra bag of lighting gear. There are times you're just gonna wanna stuff a flash by itself in the bag. You need to know the difference. David Hobby started the Strobist blog assuming everyone who read it had already mastered on-camera bouncing and were sick of its limitations. It's why Lighting 101 can sometimes overwhelm very quickly, and why he dialed back to basics in Lighting 102. Learn what you can do with a single on-camera flash before chasing after the studio-style off-camera setups.
A flash can be more transformative to your photography than a lens. I say budget accordingly. You paid $3k for a full-frame camera body. You can afford a $300 SB-700. 360-degree swivel, high-speed sync (FP), CLS, iTTL, and known decent future compatibility, service, and a solid manufacturer warranty are good things to have. A YN-560III has none of these features. Save the Yongnuo purchases for your second, third, and fourth flashes.
You may not need TTL any more than you need to have aperture-priority on the camera. But they're both highly useful things to know how to use when you do need them. Are you really going to have to fortitude and time and patience to set up off-camera lighting every single time? Or are you thinking of doing event run'n'gun with a flash, too?