You can add strut tower bars, that stiffens up the chassis quite a bit. Then run near the max spring rates before the chassis twist starts to become an issue, say 250-300 in/lb springs. In order to make that stay flat in the corners you'll need some big sway bars. Then you need to make the suspension adjustable to keep the tires happy. Camber plates and adjustable control arms/TC rods gets you most of the way there. At this point you'll have a pretty fast car. I basically ran my car about like that and I had a couple 2nd overalls at track days and autoxes.
I finally got tired of running a compromise setup and am in the process of going the full cage route and I'll up the spring rates considerably and get some real shocks on there. I've also reengineered the suspension to a large degree, and modded the sway bars and control arms quite a bit. You can see basically what I had and where I'm going on my project thread: http://forums.hybridz.org/showthread.php?t=117235
Don't get me wrong, the car was fun before, but I would have saved a ton of $$$ had I just done it right the first time or better yet I could have purchased an obsolete 240 GT2 car. Those might be harder to come by now that the Z has been reclassified to GT3, but you might start with an ITS car that needs some freshening up. Then you wouldn't have to shell out for the cage, and I've seen some pretty amazing deals go by over the years. I could have been driving for the last couple years instead of working in the garage, although I suppose you could argue that now I know it's all done correctly, or at least to my own satisfaction.