Toyo Tire Proxes TPT were the worst tyres I've owned. Poor in dry and wet pavement. Poor steering response. I replaced them with ContiSportContact2. Bought them from 4wheelonline. These tyres have awesome grip. Quiet and predictable in all conditions.
It can improve cornering though it can lessen your straight-line braking. Had a set of nexen tires for occasional track use. The wear was on the outside edge of the tyre so I added negative camber to improve cornering response and stability.
I would stay with stock size and just choose a well-known brand like michelin, falken tires and bfg. If you want to improve acceleration of your car, consider getting lighter wheels.