i agree with sgates on the r6... never had one personally, but have heard the same things about them being notorious for having nervous front ends - tucking and headshake = bad beginners bike as far as i'm concerned. The gixxer i would also stay away from as a first bike - they are pretty sharply focused... great bikes and awesome on the track, but may be a little too aggressive to start with.
The '00-'02 zx6r is a great 600. Performance is essentially equal to the other 600's of that year, and though it still would make an awesome track bike, it may fall a bit behind the others when pushed hard on a track by very experienced riders. I would say though that from '00-'02 it's probably hands down the best 600 for every-day street riding due to its strong motor (very good low-mid range compared to the others), comfortable seat and seating position, wind protection, stability, awesome brakes, smooth power delivery, etc. (great headlight output at night too... better than my '03 IMHO)
Of course I might be a slightly biased kawi enthusiast, but honestly from the bikes you mentioned, I really feel that the zx6r is easily the best as a beginner bike, and is the best street bike of the three period... regardless of how much experience you have. To show that I'm not TOTALLY biased, I've heard that CBR's are great beginner bikes as far as 600s go also. Though I noticed you left Honda out of your original post so I assume you are not considering one. I've never owned a CBR so I can't say first hand, but I bought and learned on a '01 zx6r and it was a great first bike. Just take it slow on whatever bike you wind up getting and ride safe!