A Brother Color Laser printer is the correct answer. Laser, because you don't want the potential mess, expense, and finickiness of ink. I got B/W, which has served us well, but if I were to do it again, I would get laser. Kids love printed photos even if they are super shitty low quality. Give them some joy.
Brother has a good reputation, is cheap, widely supported, and since it supports Apple's AirPrint super easy to print to it from Apple devices without configuration. It just shows up.
There is one annoyance you have to get rid of, disable Deep Sleep, which requires a hidden menu. Otherwise you have to manually wake the printer up to print wirelessly every time:
General Setup -> Ecology -> Sleep Time -> BACK and DOWN* simultaneously to enter secret menu -> Deep Sleep Off
*on the popular models. Check for the secret menu code before ordering your specific device.