I live in Edmonton, Alberta, Canada, and have owned both a Trek 930 mountain bike, and a Cannondale BT 1000 road/touring bike. Both frames have busted after 15 years due to fatigue.
A 13 year old is very likely to get a new bike stolen and will grow out of it anyways. I would get her a good used bike, as long as it is not stolen either.
Because of winters, rough roads, and gravel on highways, the best choice for a 1st bike is a mountain bike. I used 20 patches on a 1000 km trip through the Rockies with my touring bike because of the weight and the gravel on the roads. The road bike has quicker acceleration on the road, but the mountain bikes tougher wheels and more stable geometry make it a better all round choice. Road bike wheels get more flats and need more truing.
I think a road bike is fun to have for a 2nd bike not a 1st bike. Make sure you get 2 quick release wheels. You will rip yourself off if you don't, so avoid going to a department store. Sealed cartridge bearings are a good value too (but not for a 13 year old). I had them in my Cannondale hubs, and never did an overhaul or even an adjustment in 15 years, and they were smooth. Amazing compared to my Trek 930 mountain hubs which needed to be overhauled every few years.
I wouldn't get hung up on brands. You generally get what you pay for regardless of the brand for up to about $1000. After that, you may be paying for luxuries and the risk of bike theft makes it not worth it.
You should engrave your driver's license # on the frame and all components as soon as you get a new bike. Nobody likes defacing their property, but I've heard all the stories, and relying on an easily losable serial # hidden on the bottom of the frame is not going to help enough. The St. Albert, Alberta Neighborhood Watch program in Canada has created www.propertyregistry.com to register all property. Follow my links below for bike security information.