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EDIT: (Revised for 2018, current with my experiences since originally commenting)

The ideal and proper way, is probably more commitment to drag racing than most Z owners are looking for. Small rear brakes, like the 350z non brembo in the rear, will allow a 15" wheel. Use a proper drag slick, 26" or 28" x 10.5". I recommend the 28" for taller sidewall and to have an effect of stretching the gearing out a little bit. If the car is a manual trans, make sure you are using a bias ply slick, not a radial. Run the softest suspension you can, which means all stock or dedicated drag shocks. Align the car to remove as much negative camber as you can. Run the car at factory height so that the higher center of gravity can be used to transfer weight. Obviously make sure you are doing a healthy burnout, and slowly dial your tire pressure down after each clean attempt until it hooks. You will probably end up around 18-20ps on a bias ply. This is the best you can do. And it will do pretty good (1.4 or 1.3 60's with practice, we've done it. A well dialed in car can probably do 1.2s like this).

For a street and road course setup, it gets very difficult and its hard to say what is best. It probably becomes very sensitive to exact combos. The IRS in the 370z is particularly terrible for drag racing and/or hooking up high power. Even the slightest compression in the rear causes extreme camber and short sidewall tires cannot deform to accommodate that. Slamming the car on stiff springs and shocks removes the vehicles ability to transfer weight to the rear tires. You have lowered center of gravity which reduces its tendency to lean back, and the added spring rate and shock dampening again makes it even worse. Everything is working against you for hooking up in a RWD car setup like this. It takes traction to make more traction... without even a little bit of grip, it cannot accelerate enough to begin weight transfer or squat. Starting with the control arm angles of a lowered Z, the compression camber is compounded, going more negative with even minimal travel, even if you had aligned to a baseline of zero. Basically you are fighting fire with fire here, and you shouldnt expect to achieve anything great. If you somehow do, please let us all know how you did it!

For driving on the street, run the suspension as high as you can stand to look at it. Run the largest drag radials you can fit, on the smallest diameter wheel are you willing to run. Run the pressure as low as you can tolerate the vehicles handling at. Basically, get as close as you are willing to get to the ideal setup I mentioned above. With 18" wheels and drag radials, stock shocks and springs, and clever torque-reducing boost-ramping we have been able to get a 700whp Z to usually hook up second gear on the street. As cool as a Z looks slammed to the ground on 19s or 20s, I promise you that if you feel second gear hook at 650+whp, you will be posting all that stuff for sale.

Aside from that, if you refuse to go anywhere near it and want to go slammed and low-profile tires and big brakes... at that point all you can do is align to zeros in the rear, and run a drag radial with as low of pressure as you can tolerate the handling at (without going so low to ruin the tire or lose the bead). 1.8s is probably going to be the typical best 60' you can get like this, maybe you'll get an occasional 1.7 with practice, and I would be shocked (but intrigued) if anyone does better.

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