Lowering a Mustang is a great way to improve handling. If done correctly, it can also have a positive effect on your Mustang's appearance. You can lower your Mustang with coilovers or lowering springs.
To eliminate body flex, you may want to consider an export brace or subframe connectors. These can help give your classic Mustang's body some rigidity that will make corners seem easier. Sway bars are another great way to reduce body roll and understeer.
Another great suspension upgrade is simply to replace items like shocks and struts with improved versions. Adjustable shocks and struts give you more control over how firm your suspension is, and they can install as easily as replacements shocks and struts would. Likewise, replacing your original rubber bushings with poly versions can improve their firmness without requiring any modifications.
Not the year you are looking for? Check out these years: 1964, 1965, 1966, 1968, 1969, 1970, 1971, 1972, or 1973 for additional options.