Not sure exactly what's available for the CBR right now, but generally you want a full-sport tire like a Michelin Pilot Power, Continental Sport Attack, or Bridgestone BT-016 for sport riding. I personally always run a full-sport tire on the front. It's going to give you maximum traction when you need it most - cornering and stopping. Tires only last 4 to 5 years (miles don't really matter) until they begin to deteriorate and lose traction, so if you aren't wearing your tires out in that amount of time you aren't losing anything by going to a softer sport tire. Stick with the stock size. I agree with Rick - the pavement is really the biggest, most unpredictable, factor - be careful.
As far as dragging your toe, as noted, make sure you have the ball of your foot (not the center) on the peg. Your size and weight will also have an effect. If you are at the edge of the tire, and are also scraping things, most likely you need to change your body position and hang-off more.
If you really like sport riding, attend a riding school at a track. That's the best way to learn to go it right.
Jay