I want to start doing some trackdays in my 8, but the tires for 18" wheels are a good bit more expensive than the 17s and 17" wheels are cheaper too. Is this a good idea? The car will sit 1/2" lower and accelerate a little bit quicker too, it'd be the same as changing the gear in the differential.

and the swaybars will stiffen it up a little bit.

This should be a pretty good setup for the track, right?

Before doing anything to the car, drive/track it in stock form to get a baseline feel for it. If anything, a performance alignment would help very much for starters.

A 17x9 wheel is a great base for track days. Plenty of rubber to select from. Just try to keep the Outside Diameter of the tire somewhat near that of the OEM setup.

IMO, address springs and dampers before sway bars. Car is underdamped.