Hawk GTs & CB400s make excellent starters also. CBR400RRs are Euro only models, and are very rare in the US.
Hawks & SVs can be pricey, but decent ones can be found in that $$ range. VTR250s & Ninja250s are commonly priced there, but tend to be rough. Remember, when looking for bikes in the 250cc range...model years aren't very important. Rebels have had no functional changes over many model years, just like Ninja250s. "Baby" Ninjas were made for about 10yrs with NO changes at all, except paint colors. To my knowledge, Kawasaki only made changes in 2008, and those are usually the pricier models anyway (over $2500 or so).
Like many have said here, starting out on a small dirtbike is a great way to learn. Small Honda 4-strokes, mostly the XL & XR lines, are low to the ground, relatively low power, VERY light & manueverable, and easy to work on. For about $500 or less, you have a bike small enough for any woman, or kid above 14yrs old, that is nearly indestructible and easily saleable (as a pit bike if nothing else). However, they're usually not street-legal and too slow for traffic.
If she wants sporty...and it looks like she does, be patient something will come along in that price range. If you have access to one, starting teaching her now OFF road on a small dirtbike. Then, whatever you find, she'll be ready to brave the roads & the traffic there. I've taught 2 of the 3 girls in my house on an XR100; one's 15 the other 40. This bike was the best investment I've ever made...$600 for them to both tell me they don't want to ride in traffic. It saved me the trouble of buying/selling something bigger.