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I love my Bilstein shocks. I can't remember which specific type/model of Bilstein they are, but they handle/corner way better than the stock shocks, and they ride very well (they are NOT stiff).
I also swapped out for the C6 Z51 sway bar. Along with The C6 Z06 shocks, they will be a HUGE upgrade over what you've got now. It's a good combo that really flattens the car out in the curves without being too harsh and stiff on rough roads.
The C6 Z06 shocks are just OK. Probably fine for a cruiser car. The C6 shock bodies are taller than the C5 so if you are lowered at all in the rear you risk hitting the bump stop. I had this problem on track, but didnt notice so much on street.
For something a little more sporty, but not crazy expensive, I recommend the DRM valved Bilstiens. They handle great for the price.