Maybe newbie with questions @ '94

Hello all:

I'm looking to buy my first Corvette. Its been 55 years and I'm ready. Today
I took a '94 for the third test drive. During the first, the handling was
exceptionally sloppy. Turns out the right rear tire was substantially
underinflated. Test drive #2 was with repaired tire in light city driving
and it was decent enough to go for a longer follow-up, including highway.
What I found today was at highway speeds (up to 70) handling was okay, but
at speed the car seemed to crash over the over rough parts of the road and
got very sloppy longitudinally and the nose seemed to wallow vertically.
Again, it felt like underinflation in combination with bad shocks.

The car has 86k miles with decent Yokohamas.

Here's the question: Is there anything in the suspension (front/rear/both)
that could be worn out to cause the lateral sloppiness? Could what I've
described be symptoms of bad bushings in the front? Is the crashiness (for
lack of a better term) going over rough areas normal, or, as the owner said:
"All Corvettes I've ever driven ride real rough."

Aside from the ride issues the car ran strong and the automatic tranny
seemed smooth. I'd hate to rule out the vehicle if the flaws I've described
can be easily corrected through a routine service.

Thanks for reading this far . . .

Any input would be very much appreciated!

Oh, I almost forgot. The car's an unusual color. Sort of a plum, that the
owner referred to as black cherry.

Ed B.