http://www.system96.com/pages/circledemo/circle1.html
This is how I learned to cut circles. I use a piece of neoprene or a clean self-healing cutting mat. Clean well and brush off chips between each circle.
What are you using to support your circles for drilling? A piece of styrofoam always worked well for me, but it floats so I affixed it in a shallow container with silicone and let it sit overnight before adding water and drilling. Chips either got pushed in or brushed off and lasted a long time. I was partial to Triple Ripple bits from Kingsley North...I don't know how big your holes have to be but if they're not big enough, I'd go to core bits.
http://www.kingsleynorth.com/skshop/...702&catID=1031