For equipment...first off, regardless of what style she's riding, buy her a helmet. Make her wear it. I have quite literally have my life saved on two separate occasions because I had my helmet on. People might complain that it's hot, it makes your head sweat, it makes you look funny, it gives you helmet hair, but I would have been brain-damaged or died without my helmet. Let me put it this way - my first bad fall was when I was 17, my helmet was absolutely smashed, I drove myself home but still had a concussion, so my mom took me to the ER. She ran into the doctor that had seen me in the ER (for a light concussion, a fairly common event) a few months ago - five and a half years later, he still remembered me, based on my helmet that I'd brought in to show the ER. I just rode for the first time in about nine years without a helmet last weekend, because I was riding with a friend who had never been on a horse before and she was nervous, and since I knew the horse I was riding and trusted him, I loaned her my helmet...it was one of the most nerve-wracking rides of my life. Once you're used to it, it's very weird to ride without one. A $40 investment sure beats the cost of an extended hospital stay or a funeral.
She might want some basic grooming tools. They don't have to be fancy - a hoofpick (I like the kind with a brush, but I also have the kind that's plain metal to stick in my pocket when I trail ride, in case of emergencies), a body brush, a soft brush, a rubber currycomb, that should be enough. The Oster tools are nice because they're more ergonomically design, but they're also about three times as expensive. Horsemen have been using the traditional tools for centuries, pretty much (I looked through a reprint of a tack catalog from the late 19th century once - it's amazing how little has changed).
Beyond that, it depends. Is she riding Western, English, or both? If she's not a very experienced rider, I suggest starting in English, if possible - much better for your balance. I started in Western and switched to English, and even though I like English better, if I haven't ridden in a while I'll do Western, because I know my balance will be terrible otherwise. I ride in jeans and a pair of basic cowboy boots - don't bother getting the super-fancy ones with rhinestones and pink leather and all that junk. My jeans and boots work for both Western and English, although when I get to the point where I can ride on a regular basis and I'm riding English more, I'm going to buy some breeches and boots. Beginning equipment doesn't have to be fancy - remember, a lot of girls her age will like horses for a while, until they discover there are far more fascinating creatures, boys. Not that this will necessarily happen (my mom thought it would with me, and fourteen years later, I'm about to graduate with a degree in Animal Science because I still like horses!), but it does happen quite a lot.
If I can help you out anymore, PM me. I'll send you my phone number and I can talk to you about it if you'd like.