Greetings...

It kinda depends, but since this is a metal forum I'll assume she wants to play metal.

My first guitar was a Jackson Dinky (the guy in the music shop refered to it simply as "the jackson", only found out about the dinky part when I looked it up...after buying it...doh). Regardless of the poor name for a metal guitar; it's pretty affordable, looks pretty good, and plays very well for the price. It's basically a small cheap version of the soloist, if she happens to be a Broderick fan a blue dinky looks almost identical to Chris's 7 string (from the betcha can't play this vid), except for a few minor things like being smaller,only having 6 strings, bolt on neck.

Mine cost me £200 with a fender amp +plectrums, strap...etc. You could get cheaper but as i'm sure you know you tend to get what you pay for, dinky gives you alot of bang for your buck.
 
well, im really partial to ESP and LTDs, and to me, even their low quality stuff is really good compared to some other companies, EX: squier, kramer, some lower end jackson, ibanez, and epiphone etc. maybe try out an LTD MH-50 or MH-53? around 250 bucks and the sound and quality will last a long time. my first real guitar was an ESP LTD V200, and i kept it clean, and it never failed on me, no problems with it ever,and i had to trade it in to upgrade to an H351nt, but im going to buy it back from the guys i sold it to