I prefer acoustic sets myself...cheaper and just are nicer personally. If you can find a good set around town for a good price get it and don't look back :P Decent starter brands off the top of my head go from...ludwig, yamaha, pule, pearl, sonor(the force series), ddrum is ok...not a favorite until you look at their higher end kits though, mapex has decently priced sets, and pdp/dw
For starting though, yea, don't spend over $500 unless you somehow know for sure she'll stick with playing set.