Hi there Andy and welcome to the madhouse that is EuroKClub!
If we are talking about the same K1200's, then you will be doing well to find a 2002. The S was introduced in 2004 and mine is an October build, not many still around for sure. The GT was introduced in 2006.
The problem with running a budget K12S, GT or R is the relatively high failure rate of some expensive components which can bankrupt the unwary!
BMW offer a full manufacturers warranty on the K for about £300 per year and unless you are buying the bike as a toy and have great DiY skills, these bikes can be infuriating to own without it. I speak from experience as one who doesn't have the warranty; most in here wouldn't run a K12/13 without it.
Early bikes have an electric brake servo that can cost an arm to get repaired. The ESA suspension (an option) can also be a real pain and is not cheap to repair, in fact it is cheaper to replace it.
There are clutch woes to boot, although early bikes do not necessarily suffer from this.
High-speed braking judders and low-speed weave can point to failing ball-joints which is not a simple thing to repair and isn't cheap in a dealers.
There are many recalls on these bikes, rear suspension linkage, cam-chain tensioner, cam-chain jump guard, fuel pump flange, cracks to the rear wheel flange (not yet recalled) etc, etc. A main dealer bike will have these covered, as should one with a FBMW service history.
So, from the accumulated wisdom of owners in here, buy from a dealer with a full warranty, or take a risk otherwise. Make sure it is running sweet on a test ride and check all the functions of the ESA, the clutch, the ball-joints and the ABS (although this either works or it doesn't).
Good luck with the search and let us know how you get on.
Brian (who thinks if you mean the K1200LT or the K1200RS, most of the above is a load of old tosh
)