It depends how she wants to take the images. Like a machine gun and hope to capture the perfect shot or compose the shot and take a single image. If the machine gun approach then frames per second fps, autofocus system on the camera and shutter lag all come into play, because although camera's advertise fps, its doesn't mean that ever shot you take is perfectly in focus and sharp, that's definitely down to the camera and significantly improves the more $$$$ you spend.
If its a single shot, right camera settings, then its all possible with the right lens and light conditions.
I assume this would be outside rather than inside shots, because inside would require major $$$$$ and £200 would nowhere near cover that setup.
For £200 you could probably pick up a
second hand canon, nikon, sony etc SLR and kit lens that would get you started, on the other hand, there are some bridge camera's that have reasonable capability to capture moving objects, especially horse that won't be travelling that fast.
Its the way you take, composed the images, and camera settings that you use that'll get you the image that your friend wants.
