Type A slicks on the front with S Grips on the rear worked great for me on carpet.
That has been my setup for the past 2 seasons on a very high grip asphalt track. I am the only one who runs this setup on our track, everyone else is either all S-grips or all A-slicks all the way around. I like the slicks up front and s-grips in back setup a lot. I feel the s grips give me just enough traction and prevents my rear from sliding out. Where as the slicks up front let me really push the car w/o getting too much grip and rolling.