How much "experience" are we talking about? Most people here will preach to get a 250 as your first bike, as I'm sure you've already noticed. I started on my '06 ZZR600 almost 6 years ago, and if I were to do it again, I would still get a 600. It's not necessarily a bad idea to start on a 600, but the problem is not respecting the machine and overstepping your capabilities too early. The only issues I had during the learning process (which I suppose is an ongoing process really) is that I got overzealous a few times and dumped my bike. Nothing major, just a low side into the mud and one bad crash a year and a half ago (squiddin' on back roads). Other than that learning on a 600 worked out fine for me. As with a 250 though, a lot of guys don't keep them for long term and go crazy with mods, BUT on the other hand you see modded up 600's and liter bikes all over the freakin' place. If you're gonna start on a 600, I highly suggest getting an inexpensive used one; that way if you dump it, it's no big deal, then when you get good and used to the bike, you can go get a brand spankin' new one. Good luck with your choice.
One more note: the 250 is carbureted, whereas the ZX6R from 2003 to present are fuel injected. My ZZR is carb'd as well, but I didn't realize the beauty of F.I. until I bought my Suzuki a few years ago. Ah it was so great. You turn the key "on", hit the starter, and it just works. With carbs sometimes you gotta fuck with the choke and deal with the bike running great in some weather, but like ass in other. It's really a pain in the ass. A lot of guys still prefer carbs, but the vast majority go for F.I. I personally will never again buy a carbureted machine unless it's a lawn mower.