It is that time of year again. I usually get at least one question a day from a parent asking what kind of drone they should buy their kid. It isn't really an easy question to answer. There is a 100% chance that whatever drone that you buy them will be crashed within 6 months. There is probably at least a 50% chance that they will crash it with the first 30 days. I would say that everyone should start out with a smaller drone like a Hubsan X4 H107c. This one goes for around $60. It does not have a camera, but you can get one similar that does for a little more money.
If you wanted to step it up a notch you could go with a DJI Phantom 3 Standard. It comes with an HD camera, it uses GPS to keep its position, and you can use a cell phone or ipad to see what the camera sees. It sells for around $400.
The Phantom 4 Pro is even better than the one before. This will likely be my next purchase. It has a 20 megapixel camera and shoots 4K video. It also has obstacle avoidance.
If you end up buying your child a drone it wouldn't hurt to go ahead and get a few extra batteries. I would also recommend watching a few youtube videos before the first flight. I hope this helped and none of the information that I gave you is scientific, just things that I have learned along the way. Good luck and happy flying.
You can find out more information about drone safety and registering your drone at https://www.faa.gov/uas/