You ideally want a camera with a 70mm – 200mm lens any smaller size lenses will distort the horse.
Shoot in large fine JPEGS unless you know what you are doing when it comes to processing RAW files?
Set the ISO to Auto – Most camera technology is pretty accurate. Leaving your camera to decide on ISO means you will not have to keep checking each time the light changes.
Set camera to shutter speed priority: Set you shutter speed to 1250 – I find for a beginner this will cut 95% of camera shake and horse movement no matter how fast the horse is going.
Shutter speed is the only setting that can guarantee a sharp image. You can not do anything about a blurred image because your shutter was too slow.
While using shutter priority TV = Canon S= Nikon your camera will choose the best aperture for you.
Now set your focus to a “single point focus” and place this in the middle square for now, check your lens is set to “Auto Focus” AF and your Camera focus is set to auto tracking / alservo
Now pick a sunny day, make sure the sun is behind you lighting up your subject and start taking photos. If the day is really sunny then why not use the sun and increase your shutter to 1600 or 2000 to guarantee freezing any horse and camera shake, especially if the horse is cantering or galloping.
Using shutter priority with auto ISO means the camera automatically chooses the aperture so all you have to worry about is shutter speed and composition.