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.
I have a k&n intake. Bought one because it was on sale at 4wheelonline. Didn't notice a huge HP gain but I like the improved sound and throttle response.
I am looking for a good all-season tyre that's not so expensive like Michelin. I'm leaning towards the continental tires particularly their DWS06. Does anyone have personal experience with them? Let me know what works for you? Thanks!