As someone who tracks a similar car, 2006 GT with a Roush M90, this it what I have done:

Always a square set. First was the stock 17x8 Bullitts with 235/55/17s. Moved quickly to 18x8.5 Bullitts, first with 235/??/18s then 255/45/18s. Currently running a set of Roush 18x10s with 275/45/18s. The car has always been driven to and from the track. Because the car was a daily driver, yes even in the winter, the tires had to be some what streetable. The OEM BFGs on the 18s were decent enough while I was learning to track the car. Next was set of Nitto555s. They were an exceptional all around tire and more than enough for me to have loads of fun at the track. They are still on the 18 Bullitts today. Earlier this year while researching new tires, I was lucky enough to get the set of Roush wheels clad with Cooper tires. I've only had one track day with them, and they more than held their own. If I didn't get the 18x10s I was debating between the Nitto555 Gen IIs and the Firestone Firehawk Indy 500s. If money was no object, And I could trailer the car to the track Iwould have a dedicated set of track tires, read slicks, on light weight wheels. Will dedicated ultra sticky track improve your lap times, probably, but are they worth the extra money for just a few times a year, and will the increase the smiles/lap factor?