Your old beater car or daily driver may handle like a sofa on wheels but you can improve that and not spend an arm and a leg. Getting better control of your vehicle doesn't have to complicated or cost you a fortune and can usually be done with a basic set of DIY tools. Spending a weekend installing these upgrades will make your car more fun to drive and safer to boot.
If you car has some mileage on it, the factory rubber bushings may be sagging, stretched or cracked which will cause your vehicle to handle like molasses. These bushings are installed in factory suspension components to allow the suspension to move without transmitting this movement into the cabin but once they are loose the car will not react when you want it to. The easiest way to fix these issues is to upgrade to polyurethane bushings. These are usually available in a variety of hardness ratings and you can pick the one that best suits you. When selecting a bushing, you have to make a compromise due to the fact that comfort decreases as hardness and control increase. By far the best bang for your buck when upgrading your bushings are the Energy Suspension kits that are offered for a lot of vehicles. For my old beater pickup truck they offer a full kit of bushings for a little over $200 on Amazon .
Sway bars or anti-roll bars are torsion bars that act as a stiffening devices that help to assist against body roll when cornering. The first thing to check is to see if your car has sway bars as some lower trim models of cars come without a front or rear sway bar. If your vehicle does not have a sway bar then head over to the junk yard and find a higher trim of your vehicle. You can usually pull a used one off for about $20. Once you have the sway bar, be sure to buy new bushings and endlinks to get the full effect out of your upgrade or if you already bought a kit like above, these will be included.
If your car already has a sway bar but still rolls more than you prefer than a thicker unit may be in the books. If you have a front wheel drive car that likes to under-steer then you should upgrade your rear sway bar to a thicker unit as this will help the car stay flat and counter the under steer. If you have a rear wheel drive car, you will look to upgrading the front bar as it will help reduce roll without hindering traction. Rear bars may be upgraded in some cases but you need to be careful as they can lift a rear wheel if they are too stiff and cause spin for cars without an LSD. All wheel drive and 4x4 vehicles that transfer power to all 4 wheels can be upgraded too and they will be treated just like the examples above. If your vehicle over-steers then treat like a rear wheel drive model and if it under-steers treat it like a front wheel drive model.
Struts, Shocks And Springs
If your car feels mushy and bounces up and down when you are driving then you may need to replace or upgrade your struts and shocks. Replacing shocks and struts is a little more complicated then the rest and caution should be taken as dis-assembly of these components can be dangerous due to the pressure of the components. If your components are worn or leaky the easiest way to get the factory feel back is to install a ready made set which has all the components per-assembled and ready to go in. There are a few companies out there that make these types of sets and one example is the Monroe assembly as seen here on Amazon.
If you want to make the car handle better than factory then you can go to a slightly stiffer shock or struck like the KYB GR-2 or AGX . In many cases, you can find these for around $50-60 per corner and along with a better set of springs they will give you better dampening and control. If you decide to go this route I recommend getting all of your parts together and going to a local suspension shop where they can assemble the springs to the struts without danger. There are coil spring compressors out there but they tend to slip and slide and can be dangerous so I recommend against them. When choosing your struts and spring you will want to do some research and match your dampening and spring rate to your vehicle and your goals.
Engine, Transmission, and Differential Mounts
The mounts for your vehicles drive train are often overlooked but are important as they can affect the handling and the performance as well. In many cases when the mounts wear out you may hear and feel a clunking when changing gear or accelerating. These can affect your car handling and it can even affect performance if the engine feels a false knock or misfire. You can usually upgrade these with polyurethane units and often times you can get an inert for quite a cheap price that just replaces the factory rubber part. This setup from Energy Suspension gets you an upgraded engine and transmission mount for less than $100.
Once you have made any major suspension change, you will want to do an alignment on your vehicle. If you do all the parts at once, then a single alignment once your are done will suffice. If you are upgrading piece by piece then one of those unlimited 6-month alignment deals may be a good option as it will allow you to go back and re-align for the changes as you go along.