In this article I will start breaking down and describing the various suspension components, and how changing them effects handling.
Lets start with spring rates. By stiffening or softening the springs on a car you can dramatically change how a car handles. In general, the stiffer the springs are, the faster weight is transferred from side to side and from front to back. This is a good thing as the car will reach a constant state of driving much sooner and is far easier to predict. The other benefit is that with less suspension deflection/body roll in a corner, generally the straighter you can keep your tires. However, if a cars suspension goes too stiff, the rapid transfers of weight can cause the car to lose traction very suddenly and very catastrophically, often times sending the car into a hopping skidding slide.
The interesting thing about spring rates happens when you set up the front and rear with different sets of springs.
For example. If you use stiffer springs in the front, more weight will end up being transferred in the front then in the rear, due to the faster weight transfer rate and due to the fact that the increased loading on the outside front tire will also load the inside rear tire with it's cross weight. This means if you make the front stiffer you are going to end up increasing the understeer on a car.
If you stiffen up the rear then the same principle applies, only this time leading to an increase in oversteer.
The anti roll bars work the same way to increase weight transfer rates and are used to tune a cars over/under steer. Only they have the added bonus of not upsetting how a car transfers weight to the front and rear. To optimally set up a car the correct choice of springs that won't bottom out under heavy braking/accelerating as well as the right stiffness of sway bars to dial in the right amount of over/under steer is needed.
One of the drawbacks to sway bars however is that using them somewhat limits just how independent the suspension is. For example if you hit a bump with one wheel, the sway bar will transfer that bump and it will effect the other wheel to some degree as well.
Next comes damping, without shocks/dampers all cars would bounce and wobble as they drive down the road as if they were riding on springs... because they would be haha. Shocks remove the excess energy from wheel/body travel to keep the car level and ready for the next bump.
There are 2 main types of damping. These are bump damping and rebound damping.
Bump damping is the amount of resistance to suspension movement in the upwards direction. Too high of bump damping and your car will hit bumps very hard and transfer lots of upwards force to the vehicle, this excess force will cause the vehicle to "jump" a little. If bump damping is too low, then too much energy will be stored in the springs and this can also lead to "jumping" if the bump doesn't end right away.
Rebound damping is the amount of resistance to suspension movement in the downwards direction. This is part of damping resists the reaction to suspension movement. Too high of rebound damping will lead to your suspension not returning fast enough. This can have 2 problems. The first is if there is a sudden drop in the road, the suspension will not conform to it fast enough, and the second is if you hit multiple bumps quickly, their combined effect can end up bottoming out your suspension. Whereas too low of rebound damping will lead to the suspension over reacting and again can cause the car to "jump"
Proper damping selection is highly dependent on the roughness of the road as well as the stiffness of springs used.
Finally, I'll end this discussion with bump stops and variable rate springs. Bump stops are used as a final increase in spring rate to prevent a vehicle's suspension from bottoming out. They provide added depth by allowing the car to use softer springs to take bumps easier while providing the stiffness needed for hard cornering. Another way to achieve this effect is by using variable rate springs that get stiffer as they compress.