A little more information would allow for better answers. But this is the season when a lot of people are asking this question, so a few comments might be welcome by anyone reading a post with a title llike "beginners camera." I would guess your 16 year old daughter really is just starting to take pictures with something very basic, like maybe a her cell phone.
A camera that allows for trying out a lot of different things would be good. Pets, landscapes, trees, sunsets, some clouds, flower closeups, birds across the yard, sculptures, buildings, cars, friends. Let her explore and find her interests. A good camera for that would be a "bridge camera" like a Canon SX40 or SX50. Or a Panasonic FZ150 or FZ200. Also a Nikon P510, but the video is not quite as good on the other choices.
Maybe I am suggesting cameras that are a little more expensive than you have in mind. In that case every manufacturer has models a little less capable for a little less money.
I live next to a university and I frequently go jogging across it. I have observed many young men and women taking photographs. The women almost always have a large camera like the Canon SX40 or or Nikon P510, or a basic DSLR with kit lens. The men almost never have a large camera. They usually have a "travel zoom" like a Canon SX260 or Sony HX10V. My theory is the women feel like the bigger camera is a "real camera" and they don't mind the size because they are used to carrying purses. But the men don't like carrying a bag and they want something that will fit in a pocket.
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