Hi Ryan, and welcome to the forum.
I'll let the other jokers give you grief about first posts without pics.
From your post it seems you've had some experience with street bikes, so you probably know the basics and are asking for specific maintenance quirks of the FZ6. You also didn't mention the history of the bike. There are several other issues I won't mention now, that you should look at if the bike sat unused for the past few years.
The only quirky maintenance item I know of is to lube the ends of the shifter linkage, especially if the bike gets washed frequently. If neglected, the shifter will get very balky particularly if riding in colder weather. For me the problem was with downshifts. I've seen others complain of problems with upshifting too.
Spark plugs were to have been replaced at 8K and 16k. You might want to check them. While in there, check the leads to be sure they are tight. Some people have seen problems where the leads get loose then burn off the wires but the bike still runs - but not smoothly.
http://www.600riders.com/forum/fz6-...spark-plug-caps.html?highlight=cure+vibration
The other, standard, things are - depending on what the previous owner did or told you he did:
Change the oil, change/flush the coolant, change the brake fluid - particularly if it's looking more gold than pale yellow.
Check the tires for damage and age. Depends a bit on how you ride but old tires, even if they still have tread, will not hold well in corners. Check the pressure - every few rides.
Your bike is coming up on the 24,000 mile mark where the 1st valve clearance CHECK is suggested. Most bikes don't need adjustment at this stage.
Performance quirks:
The clutch engagement zone is very narrow. You'll get used to it, but after stalling more than a few times.
The more performance oriented guys complain that the forks are too soft. You can see many threads on here about higher viscosity oil, better springs, valves, or R6 fork swap outs.
As a result of FI, the throttle-to-on response is pretty abrupt. It also backs off pretty quickly so that you feel like you have to hold a steady position on the throttle.
The speedometer will read higher than actual. Mine was reading 4.5% high and perhaps because I'm an analytical chemist, this bugged the crap out of me. I solved it by getting a SpeedoDRD - similar to the SpeedoHealer. Of course this means my odometer is now reading low, but that won't get me a speeding ticket - or grumped at by my wife.
http://www.600riders.com/forum/the-...e.html?highlight=what+did+you+do+with+my+wife
Enough for now.
Chris