There is no wrong way and right way. I have always sewn from one end to the other, starting with the middle of each side. In my mind, starting in the middle gets the most difficult lines out of the way first while there are no other stitching lines to worry about. I have never even thought about quilting in circles (squares), but it seems to me that is less supportive of your batting. Usually you need to cross lines in order to meet batting specifications for how apart quilting lines need to be; the distance between quilting lines is in all directions, not just one.
One problem I ran into at first was getting puckers where I crossed stitching lines. I found that heavily starching both the backing fabric and the top helped a *lot*. I use a 1:1 solution of Sta-Flo liquid laundry starch and water on the backing (I "paint" this on yardage with a large wall painting brush, toss in dryer, and iron with steam) and lots of spray starch on the top. Starch stabilizes the fabric so that you do not inadvertently stretch the fabric as you quilt (which is what causes fabric to fold over and create a tuck or pucker where you cross a line).
Spray basting with 505 also helps because it keeps all 3 layers of the sandwich in continuous contact.