*cough* I bought a 2003 ZX-6R as my first street bike, and I grew up on dirtbikes, too. its not "night and day" difference... there are just a few things you have to adjust to. For example, leaning with the bike is no longer a bad thing when cornering, You cant stick your foot out on the corners, exc. I didnt take a safty course or anything like that, although I would still recommend it. I am a true believer in knowing as much as possible, and any place you can gain knowledge is a good place to go.
I am sure you can handle a 600CC bike if you grew up on dirtbikes. The problem most beginners have with 600CC bikes is not understanding the capabilities of a bike, or knowing the limitations. But, having grown up on dirtbikes, I am sure you know all of that.
and remember the most important lesson of all... It isnt what YOU do on the road that makes the road unsafe as much as what the cars on the road do, and how they respond to you. Remember... Cars dont try to run you down while you are riding in the woods.
Be safe, learn all you can, and dont buy into the whole "Ninja 500" thing. If you grew up on dirtbikes, you will be fine with a 600. Not only that, but you will most likely get bored with a smaller bike EXTREMELY fast.
The advice you find on this forum is usually geared toward a new rider (not a dirtbike rider) due to the fact that a lot of people on this board have not grown up around dirt bikes, and do not understand the similarities. However, once you set aside the disputes over weather or not you can handle a 600CC bike, the advice they offer is top notch. The gear, the courses, exc.