I have a 98 W202 C200 Sport which is utterly stock. It has standard sports suspension (20mm lower than the other lines) and 16 x 7J alloys fitted with 205/55 R 16 W tyres.

At first I was very disappointed with the cornering ability of the car, having read that it was as grippy as an E36 3-er BMW. I found it suffered exactly the symptoms you have all described at moderate to high cornering speeds.

However, as the weeks have gone by I have pushed the car a little harder to see what happens. It performs far better the faster you go. In particular taking a high corner entry speed and maintaining it gives more rewarding handling than accelerating through the bend. I have also found the car to be quite adjustable with the throttle. Also, when it does go, there seems to be plenty of warning and it never suddenly spins, it just steps out half a foot or so (there's a hostage to fortune). The car is rock solid at speed.

However, it does not like snow and ice at all. I would be very wary of fitting wheels of diametre greater than 17" to this car as such sizes will have very little compliance in the tyre itself and this may be quite at odds with the spring/shock set up. I'm certainly no expert, but I would have thought that the tyre profile is an important factor to consider in the context of springs and shocks.