There are lots of ways to make circles, I recommend using a die cutting method for that many, such as an Accuquilt Go.
The real problem comes in stitching them down. Doing that many small circles by machine is going to take some time as you will have to go around each circle. Keep the background small if possible and the moving around of the fabric in the machine will be easier. Stitching them down by hand will also take some time. But in my opinion, easier than machine stitching. Only you can decide which method works for you. I once appliqued over 600 yo yos to background for a quilt. I did by hand, while watching TV. Makes for great handwork.
Love the quilt by the way,