Generally you would want to go with first or second owner so "history" of the bike is not lost if you can manage that. First thing to ask is probably if the bike was ever dropped. Unless you get definitive "no" to your first question, assume it was dropped at one point in its life. At that point check the frame, engine mounts for obvious abuse. Look to see if anything was "painted over" in those areas. Check the forks for obvious signs of leakage. Ask when was the last time they performed basic maintenance on it and if they still have any records of maintenance items for it. Check the chain's condition to see if it has correct tension, in good shape, and is lubricated. That generally indicates if the bike is well cared because most owners ignore this part of the maintenance. Ask the person what s/he uses for chain maintenance. Anybody who is taking good care of the bike will whip it up and show it to you, tell you exactly when s/he did it and will not even think about it. If s/he can't, then you need to examine the bike little more carefully. This also requires more knowledge of the bikes in general, so......
If you are uncomfortable about venturing into this on your own, I would say best thing to do is have somebody you trust who is more familiar with these types of bikes to look over the bike. I don't know how you are with your local shops over there, but, sometime you can pay few bucks to get them to look at it. If the person you are buying from does not agree to this, walk away. That is definite indication of something is wrong with the bike the seller does not want to reveal. Even if you don't do this, just asking about it sometimes will help just to see the reaction of the seller.
I know some folks will hate me for saying this, but, if you can find 07+ models, go with that. They have less issues with the engine. Older models may need TPS replacement and valve recalibrations (because older models will very likely be in the range of mileage where it is required). Since you are saying that you are not familiar with bikes all that much, you will have to pay somebody else to do it (which means you are actually paying more for the bike than just asking price).
FZ6s are great bikes and can take a lot of abuse. So, there is really no list of things to look for on them that is more problematic than anything else. So, you just want to get a well cared bike, which means, the seller's attitude towards the bike is great indicator of how well it was taken care of. If you are comfortable with the seller's attitude towards the bike and seller can show you how s/he maintained it, you will very likely end up with a very solid bike that will last you for a long time. If the bike was really abused, like anything else, it will give you problems because of lack of proper maintenance. Extremely cheap price on the bike will usually mean there is a hidden problem with it. Always investigate further if the deal is "too good to be true."
Good luck with your search!
