When you design how to light children room keep in mind to use as much natural light as possible. Writting desk must be near window so your child can stundy most of the day on natural light. At night I would use spot lights, each directed in spots which are mostly used such as wardrobe, writting desk and bed and aditional table lamp for studying.
I like modern furniture so I feel lights should be contemporary. I don’t like very childish lights and also when your child gets older you will need to replace them becouse they will not look good anymore. Some modern timeless Scandinavian design will last longer. Great and affordable company I love is Nordlux. Here are their prices at one ot the Slovenian web shops called Opremisidom.