There is plenty of help on the 'net, search for things like
suspension set up
torsion beam suspension
independent suspension
Wheel alignment, wheel caster, wheel camber, wheel toe in or out.
All of which which will give you a good idea about suspension and how it works.
To make a car handle better, we are talking about corner speed, yes?
To achieve a faster corner speed while maintaining grip there's a few things to think about.
Centre of gravity,
The higher up the weight, the easier it is for this weight to affect the travel of direction, you'll never rid the car of all this weight, but you can move it.
So, lowering maybe the first step, but now you have this weight lower, how does this lower weight effect the car when it shifts? As the body weight will still shifting from one side to another (and bounce back again several times) in a corner.
To counter this, not only have you lowered the weight, but you some how have to restrain it from, a) moving about in the first instance, b) bouncing back and forth in the same corner.
Stiffer Anti Roll Bars will help with a and b.
Stiffer springs will also help with b.
How the tyres contact the road.
This obvious one will be more is better, wider tyres have more contact, but in a bend the cars weight will transfer to the outer edges, effectively loosing contact area, the wheel alignment helps, camber, caster and toe affect how the wheel (therefore tyre) sits and operates.
(FWD cars' rear wheels will generally toe in as they are pulled along and out by the front driven wheels, A NasCar will be set with geometry for always turning left!)
Other items also effect who this works, like wishbone bushing and how some parts flex or move.
So you've got the weight lower, stopped it shifting around and have a nice wide tyre contact.
Now you need to keep the trye in contact with the road.
A tyre skipping or leaving the road is useless, so over rough roads, bumps etc, you need the suspension to return the tyre to the road quickly.
Decent damping is required.
Shocks damp the bounce and disapate the energy, Stopping the suspension rebounding to often or at the wrong frequency.
Common these days is the gas shock. A chamber with oil under gas pressure in which a rod with a valve on the end moves through.
Type and thickness of oil, size of valve, gas pressure and area (for heat disapation) all effect how they work.
Different types of suspension work better than others, independent works well, both front and rear (like the Ford Focus)
Double wishbone is better, but suspension travel is greatly reduced., (like F1)
Torsion beam on the rear (like the Panda has) may be cheap, but it doesn't work well at keeping the tyres in good contact (flat) with the road at speed.
Perhaps my reasoning behind the comment, look for another car!
