When I applique circles, I use a long running stitch just inside the edge, leaving long tails with the thread. Then I place a circle of mylar (whatever size I need) and pull the ends of the thread over the mylar circle. That draws the edges up, and when you iron the circles, the mylar forms a sharp crease to sew to. I usually make multiples, and leave the mylar in place until I am ready to applique them. This helps to keep the edges sharp.
You can make circle templates of whatever size you need by drawing around the outside edge of any cirlce-shape. I have used coins, glasses, bowls, coaster lids, cd's etc to get the size I wanted.