It makes sense to look at how the cars were engineered when they were new as compared to what we want from the car today.
In 1964, the buying public seemed to want a really smooth ride. Handling was not much of an issue until the tire technology improved.
The suspensions and steering were designed around the limits of the tires on the market. Soft torsion bars, weak shocks, easy effort steering is common on many cars built back then. If you take one of these cars and simply add a set of modern radial tires, you will start to see other areas that can benefit from improvements. The alignment settings need to be changed with wider radial tires to get the most from the superior tire design. Anti-sway bars will keep the car from leaning too far in the turns. Frame connectors help reduce chassis flex from the stiff torsion bars/sway bars. Urethane sway bar bushings, a welded K member, gussets on the lower control arms, Monte Carlo brace (This is a triangle gusset that connects each shock tower to the firewall)....Many of these things are total overkill for a nice street driver.
In short, a few small upgrades including tires and a modern alignment often will improve the feel of a classic car without draining the wallet.