I would recommend starting in the middle of a top/bottom and doing all the vertical lines first, but starting from the middle working out to both sides. Then do all of the horizontal (side-to-side lines), again starting in the middle and working out to the ends. I recommend doing the long lines first because then, when you go to do the shorter lines, you won't have so many lines to cross (and create potential puckers).
I do not think it is necessary to change direction with every line but, if that is the easiest way to manipulate the quilt sandwich it should be fine.
Have you create the quilt sandwich yet? If not, I recommend that you starch the backing fabric heavily before layering, and also spray starch the top. Starching will stabilize the fabrics so you will be less likely to get puckers.
If the sandwich is already made, I recommend laying out a large sheet to catch overspray and spray starching both sides several times. (Spray, wait to dry, spray again, etc. before turning and doing the other side.) Again, the starch will help stabilize the fabrics.
If at all possible, use a walking foot for the lines. Your greatest problem will be puckers on the back where your quilting line meets a previous quilting line. Using a walking foot and starching heavily will help minimize this problem.