Hi Mate,
First off there are many more knowledgeable than me - I have only had my 'K' for a year but this is the approach I have taken.
If your bike is running and working fine then it is fine
. That said I would think unless the previous owners have been meticulous there will be a certain amount of servicing and recommissioning that will make the bike as good as it can be. However, unless there are really bad symptoms that concern you, I would be riding in the meantime and doing the work gradually as time and money allow. After all inactivity is not good for a bike.
Servicing
The starting place for this is the BMW maintenance schedule; replace brake fluid, check pad depth and caliper action; relube clutch cable, replace oils (engine. final drive, etc); lubricate the splines (if you have no fairly recent record of it being done), replace fuel filter, check headstock bearings and so on (there is more
). This is all written in the manuals and can be downloaded from the site once you have access - ask Bert (Crazy Frog) in a PM for access to the Downloads section.
Recomissioning
Any K is over 20 years old so again unless meticulously maintained some things will not be as good as new. First to go are the rubber parts. I replaced all of mine but you could inspect and replace only those with perishing pr that are split. I'd start with fuel lines, first those outside the tank and the crankcase breather hose (it often goes) and then the TB rubbers, and fuel lines inside the tank.
These bikes DO vibrate to varying degress and are well known for it. I spent ages optimising mine and it still vibrates. By that I mean there are tingly vibes through footpegs and bars at certain revs - nothing more and the thing certainly should not be shaking violently! It is up to you how much you try and remove the vibes. I would just do the maintenence as per schedule and the recommissioning and you might find the vibes subside a little. I think if you make sure the rubber parts of the induction system are in good shape (TB rubbers/crankcase breather hose) then the priority is valve clearance checks first (engine cover off job) and then engine timing (I borrowed the BMW tool there are thrads in the 'How to' section).
In 12 months I have done about 90% of the above so just enjoy the bike and chip away at it!
Hope this helps
Cheers
Dave