Where are your eyes focused when longarming? Are you looking at the needle or where you want to go? When I am longarming I try to keep my eyes focused a few inches ahead from where the needle currently is. I focus on where I want to go not where the machine is at. I do constantly catch myself looking where the needle currently is and that is when I mess up. I often will use the piecing as a guide, like aiming for an intersection of seams, but if I am quilting in large open areas I need to mark. Perhaps while you are learning and only renting time you might want to try marking your quilts so you have a line to follow. Or mark a registration dot so you have something to aim for.
Also don't be afraid to move the machine head with a little speed behind it. When you go really slow, circles often end up being "squarcles".