If you are removing the standard soggy suspension and replacing it with far stiffer coilovers, you will shift all the movement from the soggy sprngs/dampers to the worn bushes.
So the car will be stiffer...but still non-too precise.
If you really want to tighten things up, switch to new rubber bushes at the very least...preferably uprated bushes.
I'd suggest lower arm (front and rear) bushes, rear beam mount bushes and front anti-roll bar bushes.
I wouldn't bother with front crossmenber bushes - they are a pig to fit and make little difference.
If you are fitting cheap, stiff, coilovers, I'd suggest not bothering with uprated anti-roll bars as the dampers will likely be too stiff to let the ARBs work properly.
In all honesty, if you really want a handling increase, decent spring/damper/ARB upgrades will give a better handling car than cheap coilovers.