A body suspension feel???

When all is correct, these cars actually drive pretty nice.
That said, they're fifty years old now... First and foremost, make sure everything is in good condition: ball joints, tie rod ends, control arm bushings, idler and pitman arms, strut rod bushings... you get the idea.
Next is your alignment. Slant 6 cars with 78 series bias ply tires aren't set up the same as what you need for modern, possibly substantially wider radial tires- this opens up a whole host of weird tracking issues among other things. Go to a good alignment shop and follow the SKOSH chart on this site.
Following the SKOSH chart - your experiences? | For A Bodies Only Mopar Forum
Next, do you have power steering? Chrysler tended to over pump their steering, sometimes making them feel "light" and "floaty". This gets amplified in the light A bodies. The solution? Dial down the assist: Pump It Down....EASY | For A Bodies Only Mopar Forum
Once you're done with all the above, you'll be shocked at the difference just "optimizing" what you have makes.