The best thing to do is take DD out and let her try on a few in your price range and see what she likes. If DD is 12, you might not want to spend a whole bunch since she will be growing and in a couple of years you'll be dong it again. If she's older, you might want to invest in something a little more durable.
Suggestions:
Mizuno GXS53 Around $80-100
Mizuno GXS31
Wilson A2000
Worth Liberty All around $150
These are good mitts, break in fairly easily and will last a couple of years of hard use.
Nokona
Akadema
and my personal favorite, Vinci will run $175 and up. They are hard to break in but will give your DD many years of hard use if properly cared for.