Certainly some cables are better, and you need to choose to fit the task. The short ones with a mic are great for using with a phone. For longer runs, you should use one of the ones intended for carrying line out. Look at Amazon under what Monoprice has for the best deal relative to the quality.
As for the colors, I don't remember which is which in there, but you have to get it right. You can probably tell by looking at the positions on the jack as to which part of the plug it conducts with. They're called TRS connectors, for Tip Ring Sleeve in order going back from the end. The tip is L+, the ring is R+, and the sleeve is common -. When you're in the headphone cup, you should be able to tell which color is which by looking at what goes where. Twist the wires on to the jack's terminals, plug a cord in and play through them and verify that both drivers are working before soldering. Be careful and methodical about it, and you'll get it done.