Hey Foxy,
Welcome aboard.
At 5'4" you are right at the point that your height is gonna make or break you as far as what bike you can pick.
The 2000-2002 ZX-6r has a 32.3 inch seat height.
The 2003 ZX-6r has a 32.5 inch seat height.
The '03s are a little narrower, so on them depending what type of legs a person has (thin, beefy etc) can make the 03 a little easier to sit on.
On a sport bike you can't have too much heel on your boots or you won't be able to work the rear sets right.
To answer your question about speed, if you have rode on a YZF600R, that is the non-racing R6 basically and it's seat height would be 31.7 inches and yes that bike is fast (Not as fast as the R6) and the Ninja would smoke that bike in a heartbeat. The Ninja and the R6 are pretty even speed wise in the 00-02 years, but in the '03 the Ninja takes the R6 hands down. The ZYF600R though cannot take a Ninja 6r in any year. LOL
Now, gonna change the mood here. Now if you are 16, I wouldn't think speed should be your first thought when getting a sport bike. Especially for your first bike. You would want to concentrate on honing your skills (amd looking good of course) and preping yourself for your "next" bike. And that goes for all of us and whatever our "first" and "next" bikes are.
How did you feel sitting on the YZF? Both the Ninjas would be slightly taller. You need to sit on the different bikes and see how they work for you. Some bikes require further lean to reach the handlebars and also the seat to peg distance is different from biek to bike so you have to take all that into consideration when trying selecting a bike.
Now, not to steer you in another direction, but have you considered a Ninja 250? It's not as wimpy of a bike as you would think. I had a Ninja 250, and I trained an ex GF how to ride it and she also took the MSF course as well. Now she was 5'2" and the Ninja was just right for her with a 29.3 inch seat. Also the Ninja 250 will cruise nicely at 80 MPH with two people on it. So it is a very capable bike and a great starter bike for guys or girls (especially girls) and also is great for someone that it not super tall. Also you can get into a 250 for under 3 grand and ride it for a year and still sell it for close to what you paid for it.
So I hope all that helps. Let us know what you decide.
-Flash
PS: My new girlfriend is 4'11". [

] She couldn't even sit on the Ninja 250.
(insert short girl joke here) We even tried a Derbi replica, no go, she is just too short. So we had to get her a 50cc scooter. She was watching me type this and she said she'd love to be 5'4" and would gladly change places with you.

LOL