That scooter that LasPalmas has is a very good option, to be honest. They go 95 km/h (she won't be allowed on highways as a beginner IIRC), has underseat storage, looks good and gets great gas mileage. And insurance will be cheap since it's only 50cc. Add in the fact the licensing procedure is easier than a true bike and it's the way to go. All for about $4000.
If she really wants a "true" motorcycle, the new Honda CBR125 gets my vote. Cheap to insure, cheap to buy, very light, very stylish, good on gas (2L/100km)...and here's the best part. If you buy it new, they have a new rider thing. You get protective gear with your purchase. Helmet, jacket and gloves. Very nice. I've ridden one to try, and must say, it's a VERY good package for a beginner. So easy is this package to ride, they have a race series for riders UNDER 16 years old. Again...all for under $4000. Get a nice armoured backpack, and she'd be all set to carry her books.
But my personal favorite is some kind of dual sport. Essentially a street legal dirtbike. I like these for very new riders because you can beat the living crap out of them, drop them, crash them, and they just don't break much. A Suzuki DR125 or Yamaha XT would fit the bill. Again...very cheap to operate and insure.
Whatever you decide on, enroll her in a motorcycle training course. THIS IS A MUST. NON-NEGOTIABLE. The course is VERY, very good. They teach you on bikes in a HUGE parking lot on easy to ride bikes. It's invaluable, and some insurance companies insist on this. I insist on this because she will learn sooo much. YOu want her learning in a parking lot for the first little while, not on a road. FWIW, I was a fill-in instructor for the MTO course in Windsor. Here's a list of colleges that provide the course:
http://www.mto.gov.on.ca/english/dandv/driver/gradu/motocourse.shtmlSo you have a few options here. Motorcycle training course is a must first. Insist that she take the course if she wants your help in purchasing the bike. Again..IMO, this should be non-negotiable. She either takes the course, or no bike. PERIOD.
If her riding is only in town use though...My vote is for a scooter. Below is a pic of the Honda.
CBR125: