I'm going to go ahead and kind of contradict what some of the others are saying here. Bear in mind this is my personal opinion.
Having ridden my friend's Ninja 650 for a couple of months, I hadn't owned a bike myself until 2008 and purchased the FZ600 as my first bike. I was in the same position as you, knew how to ride it (even took the class and had my license), but didn't own yet.
With that said, the Fz was the only real option for me, and it ended up being perfectly suited to my needs and skills. Depending on your mindset, yes this bike can get you into trouble, and even injure you (or worse). This is no different than any other bike though - so the mindset you ride with is really crucial.
If in your car you have a lead foot, lots of tickets, like to go fast, even a few accidents maybe - then riding on the street might not be for you. Being sensible and responsible at all times is 100% most important aspect (for me). If you follow those guidelines and are a safe rider, then I see no problem with the FZ being your first bike.
Everybody told me not to buy new, and go smaller. I knew i would be bored with a 250 because of my size and weight, so this was my first bike and I have no regrets, 2 years later. I have 0 accidents and 0 speeding tickets, going on 14,000 miles (knock on wood). This bike sweep you off your feet on the turns and give more than enough power for highway use. Just use it responsibly (because your life depends on it!), in which case I would say the FZ600 is a terrific beginners bike - it worked for me.
There's my 2 cents.