Factory Z34 race car runs 18 x 9.5 all round, with 250/660R18 slicks - see specs at
NISSAN FAIRLADY ZNISMO RC
I run RAYS 57 18x8.5 front with 245/45R18 and 18x9.5 rear with 275/35R18 rear which:
a) lowers the car ~20mm (my ride heights are 690mm front and rear - to top of wheelarch)
b) lowers the CoG by 20mm for improved mechanical grip
and gives me access to a reasonable range of tyres (although you in the US are much better served with selection of R-spec's and stickies in 18" and 19")
I bought the RAYS off the Oz-forum for a good price (around 45% of dealer sticker price for new ones) and they were undamaged and near new - less than $400/corner for a great wheel (strong AND light).
I use Direzza for double duty (occaisional track day and DD), but if going for ultimate grip, would use Dunlop slick in 250/640R18 in SS12 or D12 compound for sprint races and D11 or D21 for enduro (anything longer that 25-30 minutes). For R-spec, take your pick, Toyo, Yokohama, Dunlop (mostly Japanese-spec), BridgeRock, Pirelli, Hoosier - lots of choice in the US, but more limited choice over here.
Personally, 10 and 11" wheel widths put too much tyre on the car whereas 8/9 or 9/10 and 245/265 or 245/275 let you "Drift" the car - more rubber creates more grip but ultimately the breakaway is more abrupt (IMHO). The factry clearly tnks a square setup is the way to go (at least in the FIA GT4 category the NISMO RC is targetted at).
In our race category, <1200KG race weight limits total wheel width to 40" in any event, and we are not permtted to race with FI, so we'll always be power to weight constrained and getting weight out of the car is cheaper than adding horsepower to the engine ....