Why are you looking at the Ninja (636 i believe) and not the fz6? The ninja actually has more displacement, and is just a powerful/light. If you're looking at the small ninja for her, I would think the 250, maybe the 500. IMHO
Simple answer is that the Ninja 650 is a two cylinder with counterbalancers, and while I haven't seen specs published yet, its seat height, width at the pegs and weight are reported in reviews to be low, narrow and light, respectively. While I think a Ninja 500 (or EX500) is a better first bike, especially since it can be found used, I think she'd grow out of the Ninja 250 too quickly. Moreover, I firmly believe that the Ninja 650 is likely to be MUCH preferrable to the FZ6. Here's why:
The FZ6 sports something like 90 peak HP, and is taller than the Ninjas mentioned. I believe the new Ninja 650 is supposed to be around 70 HP (still considerable), while being at least as compact and light as a Ninja 500.
More importantly, the FZ6 is a 4 cylinder, while the mentioned Ninjas are 2 cyl bikes. Many of us might not remember this (I've been riding a LOOONG time), but standing astride a bike stopped at a red light and trying to feather the clutch as she rolls on the throttle when the light turns green is likely to be one of the biggest challenges she will face for a while. All she has to do is drop it with traffic waiting, or lurch it though a crowded intersection, and her stress level will go off the charts, her fear level will go up and her enjoyment level will go way down. I want her to have the maximum advantage in becoming a good rider who learns to concentrate and handle a bike intuitively, not be scared and distracted by bike issues that clutter the mental and emotional landscape.
Displacement isn't the primary factor here. Weight and leverage (e.g., seat height) certainly play a part. BUT the main ingredient is that a small (600cc) 4 cylinder tuned to produce peak power up around 10,000 rpm doesn't have the torque at lower rpms that a 2 cylinder of similar displacement does. As a result, there's generally a LOT greater margin of error in feathering the clutch from a standing start with the 2 cyl. than there is with a more highly tuned 4 cylinder of similar displacement, which must be revved higher to get the same torque to start off. Easy for you and me; not so easy for a newbie who hasn't been clutching with a left hand and rolling on throttle with the right for most of her life.
BTW, the Suzuki SV650 would fall into the same group as the Ninja 500 or 650 IMO and can be found used, but I'm not convinced yet that its seat height is (or can be made) low enough. Still, it would be one I'd like to look at for her -- again, assuming she wants to go ahead after the MSF class. I've told her that I'll only support this endeavor if she wants to do it for her (not for me) AND is committed to becoming an excellent rider. I DO NOT want to watch her do a get off on a bike. If she spends a year or two getting to be a good rider on an easier bike to learn on, then I'd happily encourage her to sell the first bike and get an FZ6 (a bike I really like, esp. for the money a used one goes for) if that's what she still has the hots for.