Like a STi?
I would imagine coilovers in the front and 4-link rear would be a good place to start. Being as old as they are, SyTy's are really only limited by your budget.
Member HighPerformacneTrucks is building a road racing Syclone. He could probably give you a lot of insight on what it takes to make them handle.
You can make anything handle. It just depends on how much time, effort, and cash you want to spend.
i would say full coilovers, sway bars, and some good tires
I think your being optimistic that it will handle like STi (or Corvete, Evo etc.) without some major work done. (ie reinforcing frame, new front/rear suspensions and mounting points.)
Do you guys know anything about the Rear Coilovers? I havent seen that done....