Hello and welcome.
As with any car of that age, make sure everything works as it should.
things to look out specific to the S type is lurch with the gearbox when putting it into drive, make sure the gear changes are smooth and not noticeable, it's supposed to be a sealed for life unit but can be serviced and flushed for about £250.
Rough running will definitely be down to worn plugs on the right bank as they have a life of around 100k and, due to it being a right faff to change them they get left, even on dealer serviced cars!! (Search YouTube for Stype plug change to see!!)
other things to look out for is rust on the sills, they rot behind the plastic covers into the floors and if bad can write off even a 2007 car!!, make sure the heater blows hot and cold as a dccv fault closes the heater water feed, not an expensive job but fiddly!
Also, make sure the aircon blows cold as it's expensive to put right as it's usually the pipe that runs under the right bank manifold that wears out, £350+vat+fitting for the pipe!!
Try and have the car started up from cold as, although the V6 has a cam chain it's well documented that the tensioner can be noisy due to gunk sticking them up, listen for a tappety noise on startup until the oil works its way round.
Again, a flush and new oil should sort it.
Hope I haven't painted a bad picture as these cars are amazing and beautiful to drive!!
Good luck and don't forget to post pics up when you've bought it.