My coach tells me to circle to my left because it keeps the other guy out of position, and keeps me from being in front of him. However, I'm finding that the more experienced guys are able to anticipate me, and maintain their position. My plan is to mix in more feints and body/head combos.
Forwards, backwards, right, left, around your axis, move anywhere you want. Sometimes you'd avoid his left, sometimes his right, sometimes the movement is for your own offence if you're looking for angles. Sometimes you get chased and sometimes you do the chasing. And sometimes you do not move at all, if you need to stand your ground. Movement is not the goal, it's a way to achieve your goal.
Yeah I also find that people who are constantly circling and moving have a really hard time with ring control.