The 600 will drag you around, no problem. To be honest, I expect you'll be a bit taken aback at exactly how fast it is. Well, taken aback, or scared of it, either way.
Personally, I started on dirtbikes at 9 or 10, got my first streetbike at 14 and kept moving up. I have been on the gixxer grand for about 6 years now (got my first one at 22, til then I had 600's).
Get what you're comfortable with. most GOOD dealers will let you test-ride used stock. Quite frankly, the sport-bike line is uncomfortable as hell at first, until you learn how to sit and ride on them, but that's another topic. Try a SV, I'd say. They have a V-twin engine and a sport-bike inspired chassis. The big twin makes tons of torque, without all the horsepower and twitch a sport offers, which will reduce your repair bills. I've ridden them, and they're tons of fun.
Just some advice, from a guy who has been there:
1- Your wrists will be sore as hell til you figure out you're not supposed to lean on them. You grip the tank with your legs and sit on your arse, not your hands. Not only is it a comfort issue, but a sportbike isn't designed for leaning on the bars, it's actually dangerous to do so because it causes handling problems.
2- GEAR GEAR GEAR. I don't even ride to work without at LEAST heavy boots, skid-lid, leather jacket, gloves and jeans. Any riding I do other than that and I have on my padded pants.
3- Why all that gear? Because you buy a sport-bike with ONE thought in your head. YOU WILL GO DOWN. It happens.
4- For reasons stated in 3, your first purchase should be a set of frame sliders. You have been warned. My $150 USD frame sliders, over the years, have saved me probably over 6k in repair. Everything from dropping the bike in parking lots to having cars back into it, knocking it over, even to low-siding the thing a few times.
5- Don't sweat the chicken strips. I have them on my street tires, because PA roads are freakin awful. Anyone around here without strips is a suicide jockey and asking for a case of road rash. This is coming from a guy who regularly rips the center treads off his tires on the track, and the sides don't do much better. I can ride circles around 90% of the riders around here, and I have strips. What do I care?
And, last but not least, we come to 6. The one noone ever listens to. NEW TIRES SUCK. I just picked up my latest GIXXER Friday, and STILL can't really get on it because the tires are like glass, even with 400 miles on them. Break them in slow. You know they're broke in when all the tits are gone. Til then, keep your wrist out of the throttle.
Aside from that, ride a few bikes, figure out what you are comfortable LEARNING on, and get it. Don't think of it as the last bike you're gonna get, think of it as a temporary learning bike. You're going to become a better rider FASTER learning on something you aren't scared of, then jumping to something that scares the crap out of you, as opposed to just buying what you think looks cool and being scared from the get-go.
This preaching brought to you by Guilty Racing Inc