I want some new tires that perform really well. I have been looking at the Toyo Proxies T1-S and the Brigestone S03 does anyone have any thing good or bad to say about there tires or recommend any other tires?

Do you have any suspension mods?

What size are we talking?
For max performance like you mentioned
The PPS03 is the best all around street tire performer.

I feel like we cover this topic a lot. Check out the search, and search for

"what tires"

You will find many posts and good recommendations :)

Currently I do not have any suspension mods but next week I plan to buy Skunk-2 Coilovers with Koni Yellows. The size would be 205/40/17. Which tires between the Toyo Proxies T1-S and the Brigestone S03 perform better in dry conditions?

Thr S03 compound is softer, and will remain sticky and quiet the life of the tie.

The usual problem with tire questions is that you don't tell us what you want your tires to do. Do you want the stickiest tires on the street? Do you want to autcross? Drag? on your street tires? Or are you just looking for a good value that will perform well when the weather turns bad and give you a decent ride (nevermind the 17" wheels and droped suspension).

The tires that will give me the best traction while taking turns at higher speeds are the ones I want.

Falken Azenis, then, but don't expect a long tread life.
Your alignements will have a lot to do with how stable and how the tire contact the pavement under those conditions.

You are not being very specfic.

You want to race? It just sounds like you want to fly around off ramps.
What is your driver experience any seat time racing autox or road race?
or you just a hot shot street racer?