When I cut my circles, i used a push-pin to pin-down the radius point. i pinned it into a piece of lumber. then, i tied a length of rope under the push-pin and then tied a pencil to the other end such that the pencil marked the radius of my rim. then, holding the pencil vertical and steady, i was able to turn the plastic, like a record and get a reasonably perfect circle.
and a sharp blade helps the cutting process. the trick is to go over the cut 2-3 times with the knife instead of cutting it all in the first go. i recommend
this knife if you have to buy new. you can pop off the dull edges, and the handle lets you push with your thumb unlike a regular xacto handle. i used this blade for 10+ years building architectural models.
im pretty slow, so this is really the only area of expertise i can contribute to this forum.