When it comes to making circles, I prefer a simple jig like this one when I can use it. The jig works as a trammel to guide your plunge router as you cut.
Drill out two holes in a piece of plywood, one for the bit and one for a dowel. Glue the dowel into the jig. Drill a hole (or holes) in the piece you’ll be cutting as well. Once dry, attach the jig to your router (I use double-sided tape) and fit the dowel into your piece, then let the jig guide your routing.