If you're just starting out, any of about the top 8 in Tire Rack's Max Performance group will be sufficient, as will comparable tires not there if you can make the correlations.
My original Goodyear Asymmetrics (not the Asymmetric2) even with three 3-season stints and 15000+ miles in street duty plus a couple of previous track days and a little autocrossing on them were still good enough to let me run down and pass more cars than were catching and passing me at a recent 2-day track event at NJMP. And they're only 255/45-18's on 18x9.5 GT500 wheels, on a 4.6L car that has only cold air and a mild tune. IOW, don't get carried away just yet, as driver improvement is going to make more difference than there is among the better Max Performance summer tires.
If you stick with the staggered wheels, give some thought to using the same tire sizes that the 2008 GT500 used - 255/45-18 front, 285/40-18 rear. But make sure that the offsets will keep the tires inboard enough to avoid rubbing on the sheetmetal, as you'll be leaning the car over a good bit more than you do in most normal street driving. S197's generally need offsets in the ET+42 to maybe ET+50 range, not ET+22 to ET+32 which will stick a little of the wheel and tire out past the sheetmetal.