The ways chosen to wrap a ring shank depend totally on the creator. Personally, I rarely begin a full shank wrap in the center and work toward each side, because I find that often the first and center wrap isn't as tight as it should be, (which can happen when beginning a wrap), it juts out and after wrapping the entire shank there is no way to correct this.
I prefer to begin a shank wrap at one side and then wrap entirely around the shank. There are a few designs that actually call for a wrap to begin in the center of a ring, which is usually important to execute that particular design properly. If I find that I have not planned for the needed length of wrap wire and it does not go all the way around the shank, I can simply end it where it is and then go back and remove a few from the beginning to make the sides match, OR if the shank is wide, (like 4 wires), I have been successful with adding another piece of wrap wire, just by cutting and placing it to butt immediately against the end of the ended first wrap segment.
Determining the exact length of a shank wrap wire is difficult, but with some experience you will know about how much to cut, depending on both the of size of the ring and the width of the shank. A suggestion is to always cut just a little bit more than you think you'll need, because as we all know, there is always a use for a 1 - 2 inch piece of half-round wire in a future project.
Answer contributed by Dale `Cougar` Armstrong