Green is indeed the ground. You can use the ground in your wall socket. Ground everything together. The metal bracket of your socket, your reflector, the ballast.
In AC terminology, black goes to "hot" and white goes to "neutral." On the wall socket, the slightly larger terminal is neutral.
For the AC I would use a heavy-duty extension cord. Someone can correct me on this one, but I think what you want to use for the ballast leads is 14 guage wiring. If you go to Home Depot or Rona or whatever and get a "heavy duty appliance power cord" you should be OK.
I'd also use a heavy guage for the ballast to the lamp. The longer that this is going to be, the more resistance there is in the wiring itself, so you can hopefully compensate by using a heavier guage. Why make the stuff work harder than it has to.
I'll go check what guage I use on my ballast to lamp wiring. I'll post back what it is after I go take a look.
I don't think it will matter how you connect the red and blue wires to the socket. Even if it does matter, you have a 50/50 chance of getting it right on the first try. If the lamp doens't fire, turn everything off, switch the red & blue, and try again.
I don't bother with a quick disconnect for the connections between ballast and lamp. Once the ballast is connected you will rarely need to disconnect it anyways, you can use any old crimp-on butt connectors or the threaded wire nuts or stuff like that. But if you can get your hands on a quick-disconnect, go for it ... it's as fun as you make it, right?
