My daughter just got a computer for her children, ages 10 and 5. Because of the way her house is set up the computer is in the common room. She would like to get headphones because the sound from one playing the computer conflicts with the volume of the TV aka sound war. What type, or possibly even brand, would be best for a younger child?
I suggest not to buy the low cost. You must choose the good quality of headphones for their own safety. Kids have sensitive eardrums. It's a good idea if you'll buy good brands like Sennheiser and Plantronics. The sound of their headphones is not noisy unlike other brands.
I've found that there are special headphones for kids that limit the volume they output. Doesn't matter how high you turn them up they won't go above a certain level. Search for kid safe headphones in Google.