For the disks use at least 3/8 inch thick ply or some other material just as stiff. Don't use solid, non laminated wood as it won't stay as flat over time.
You need two circles with holes big enough for your bolt in the center. I cut mine with a router like this.
Start by marking out 2 squares on your plywood sheet that are a little bigger than your final disks.
Draw lines between opposite corners to find the center point.
Drill a hole at each center point the same diameter as your bolt.
Now make a jig for your router to attach too. (I said this is the hard part)
A thin board works well for this, about 6 x 18 inches.
Mount your router to one end of the jig by drilling the appropriate hole pattern and bolting your router to the board.
From the outside edge of your router bit measure across the board half the diameter of your rings and mark a center point. Use the smallest diameter router bit you can to make it easier to cut a slot in the plywood later.
Drill the center point with the same drill bit you used for the center bolt holes.
Place the board with the router mounted to it on top of the plywood and place the drill bit in the hole in the board and the plywood so it "pins" the jig to the board. Cut out the disks by spinning the jig. Cut a little bit deeper each pass and it will come out clean.