Very common for the FZS600 to clonk when going into first gear either from neutral or from second. When changing up from first to second it helps if you get the revs and speed of change just right, but most times it gives a loud clonk. They don't normally do it when going into third gear and above. I would check that the clutch is adjusted right and is freeing properly.
Some of these bike seem to suffer a small resonant vibration round the 5,800 to 6,000 rpm mark. Balancing the carbs may help. I used to feel it on mine, but now that you mention it I realise I have not noticed it for the past year or so. Now done 32k miles so maybe it's just bedded in.