If it's an applique circle, I perfer to use Wonder Under and cut it out neatly with the scissors and stitch it down. You can draw your circle on a used dryer sheet and place it on top of the right side of your fabric and stitch all the way around it. Cut a slit in the dryer sheet and turn the circle out through the slit. Carefully manipulate the edge until you get it perfect and iron and sew it down.
If it's a pieced circle like Drunkard's Path, I carefully pin it, sew the seam and clip the seam allowance curve at intervals to ease it into laying flat. If you are trying to FMQ a circle, good luck because perfect circles are very hard to do freehand. If it is a larger circle, you can machine stitch with your straight line sewing if you turn the quilt often (not easy to do if it's a big quilt). I don't know if any of these suggestions address your problem.