You can echo quilt with a regular sewing machine. Instead of doing closed circles, which require starting and stopping for each circle, you may want to consider a variation such as a spiral (or closing the circle, then "travelling" with your stitches to the next circle without stopping and starting) to avoid this.
If the design is large, I have successfully echo quilted using a walking foot. It does require frequent stopping to slightly reposition the quilt every few stitches. The advantage is that you end up with very even stitches.
The more common practice is to FMQ the echoes.