If it is minimalist functionality you want, I'd recommend a bike with an internally geared hub. For your budget, you have many options, and your penchant for more fitness/sporty options lead me to think that a fast hybrid or sport tourer would be a good match- the primary difference being flat bar versus conventional drop bar.


Since you specified km rather than miles, are you in Canda? If so, check out the MEC offerings.
I bought my wife a Hold Steady last year, and she absolutely loves it. It is a phenominal bike for the money - fast, ridiculously reliable and low maintenance, and superb quality. The xxs frame would be the size to look for.
MEC has introduced a new bike utilizing the highly anticipated 11 speed variation of the "alfine" internally geared hub (IGH for short), and it looks to be quite nice.

Other Canadian options include Brodie Ocho (8 speed IGH) and Once (11 Speed IGH), which are equivalent to the MEC offerings.

Otherwise, I second the recommendations thus far. Small frames can be difficult to fit, so it is helpful to get face to face advice based on your specific shape and preferences.

Ride several bikes representing several different styles to see what style you feel most comfortable with.