I have a 2001 Jeep Grand Cherokee Limited 4X4. What is the best kind
of shocks to install in order to maximize the stability of the
suspension. Some people say to go with factory shocks while others say
to use after-market brands. Price is not the issue, I am just looking
for the best ride.

You say 'maximize the stability.' I suggest any heavy-duty shock that
would be available at a major brand parts store, like NAPA or such.
Ask the oldest guy at the parts counter. Something for towing or with
a byline like load-leveler.