It's not just hands and arm reach, but in an effort to not sound crass, bust size and shape. My wife had wanted to try playing instruments, but she always found that placing them in her lap was always a problem due to her chest. She couldn't find a comfortable position to place the instrument in consideration of her body, and that frustration led to giving up. I'm sure we could've found her an instrument to be more comfortable and accommodating, but it wasn't a driving force in her life enough to try.
Conversely, I know female musicians who've adjusted how they hold and position their instruments to compensate, and they are of all shapes and sizes.
The actual model of the instrument is honestly irrelevant. Going to a store to find the right one that
fits and is comfortable to play, both in seated and standing positions, is more important.
Also, I agree with not leaping to conclusions that a 16-year-old girl has smaller hands. We have no idea. She may be 6'2" for all we know. Or she may be 5'1" with long, slender fingers or 5'10" with short stubby fingers. Whether she sticks with it for 10-15 years is also irrelevant. She's interested
now, so don't gate-keep. She may lose interest in 2 years, or she may not. But I guarantee that if the "oh, you can't play because....." gets piled on
now, then it's a guarantee that she won't stick with it because the cards have been stacked against her before she even gets a chance.
Go to a big store, Guitar Center if need be. Let her try some instruments out. Let her explore. She's 16. It's her first time trying out an instrument. It's exciting. Let her get more excited. Doesn't matter if it's a $100 Rogue or $200 Samick or $300 Squier.
Then, if she becomes a prodigious phenom like Tina S., then upgrade. But give her the chance to figure that out. Let her try some different instruments in person and see how they feel. Again, model & brand are irrelevant at this stage.
Price, sure. You're not going to get her a genuine Gibson Thunderbird