Congrats on the new car. I'm really liking the S197, hope you like yours too.
As far as FS legal wheels, I think the '05s only came with the 17X8 rims on the GT, so you can't legally go to the 18X8.5 rims. The good news is that there are tons of 18-22lbs wheels out there in legal size in the $125-225/ea range, so about the same as Bullitts...look at TireRack, there's a whole bunch of Enkei, Kazera, TR Motorsport, OZ options...not sure which ones are the correct 17X8 and +/- .25 offset, needed to be FS legal. You could also find some 17X8 oem take offs pretty cheap, if you look around, but they are heavy.
For autocross, a 275/40-17 will work. The Hoosier A6 is considered the quickest stock class legal DOT R out there, currently, but they are pretty pricey ($280/ea). The Kumho V710 is also a great tire, also pricey ($256/ea), but they wear a bit better. If you aren't worried about being super competitive, but still want to run a DOT R, the Kumho Victoracer is less money and wears very well...and works in the rain. You could also run a 255/40, which would give a little better turn in (it actually fits the rim better) in any of the above tires.
That's my 2 cents, anyway.