If it is just autocross, then the
American Racer or Hoosier A7.
If it is street and autocross, then Toyo R888R, Nankang AR-1 or Maxxis VICTRA RC-1.
As far as throttle response, I would start with checking your engine health. Have you checked your compression? Done the
basic maintenance? If the engine running properly, then there are still things that can be done to get better throttle response: Lighter flywheel, remove counter balance shafts, run smaller 15" wheels and tires, remove AC compressor, anything to reduce rotating mass.
I drove for 3 months with a broken intake pressure sensor, and didn't know anything was wrong until I started tuning with HP Tuners. Then I saw the data the engine was using, and the intake pressure never changed. A $30 new sensor, and all of a sudden my engine was 50% more power. HP Tuners is available for 2007-2010 2.2L Cobalts, but not the 2005-2006 2.2L.