The term you want to use is 'counterbore'. Countersink is a cone-shaped indentation in order to set a flathead screw flush or below surface. A counterbore is a cylinder-shaped indentation, designed primarily for pan-head screws, and usually drilled using a forstner bit.
For plugs, look here
. You can save yourself a lot of work by ordering the plugs, and looks like a pack of 50 birch plugs, face grain, 1/2", is only $5.99.
Otherwise, tools to make plugs are on that same page. Standard way to go is to cut a bunch of 'rings' into a board with a plug cutter, and then slice them off on bandsaw.