the k2/k3 are good bikes, no real problems, the k1 750's had some dodgy gearboxes, i've rode a few and it feels as though the chain slips (even though it doesnt)
this was rectified on the later k2/k3 models, the k4 was a smaller bike and a model change
i've rode a few dukes which handle like they are on rails but i dont like the v twin power delivery, much prefer the scream of an in line four, i prefer the 750 to the thou as its more rewarding to ride and there isnt much in the power difference in the real world, i went from 20mph to 140mph on a k3 gsxr750 with a power commander and an end can with a k5 1000 with a racefit can and i can honestly say there next to nothing in it, it suprised me i thought the k5 would disappear
just the usual stuff to look out for, chain, sprockets, and listen for cam chain rattle, the tensioner can sometime go but its very rare
overall - service em and ride em